Joan Jett jumps back

Quick, name this punk band:

They pounded the club circuit for years and released their first album independently.

They scored a breakthrough single and signed to a major label. They recently played four sold-out dates at small clubs in New York, including CBGB.

And now, for the first time, they’re one of the star acts at America’s premier punk festival, the Vans Warped Tour.

The band is Joan Jett and the Blackhearts, a group that’s been around since the early 1980s, decades before the Warped Tour even existed.

At 45, Jett is at least twice the age of the kids she’s playing to (and with) this summer, but in some ways she fits right in.

“I never subscribed to the idea that punk rock means you have to play fast and scream,” Jett says, speaking by phone while on the road recently. “To me, it means being a rebel, being an underdog, being outside and doing it yourself.”

With a new album, “Sinner,” released on her own Blackheart Records label, the time seems right for Jett to reintroduce herself to a generation that probably knows her only as that lady who sang “I Love Rock ‘n’ Roll” back in the early ‘80s.

But Jett was a “woman in rock” long before that term became a catchphrase. And she was an independent artist years before the indie-rock trend.

At her show last month at the Brooklyn nightclub Southpaw, Jett was in impressive shape, boasting muscular arms and a supermodel-smooth stomach. Wearing black leather pants and a bikini top, she hammered out 90 minutes of loud, sweaty rock to an equally loud, sweaty crowd.

“She’s a total showman,” says Kathleen Hannah, the singer for Bikini Kill and Le Tigre, who co-wrote several songs on Jett’s new album.

“Everyone knows she’s sung ‘I Love Rock ‘n’ Roll’ 3,000 times, but she can do it like it’s the very first time she’s sung it. That’s beyond talent.”

Warped Tour founder Kevin Lyman says Jett is bringing “some style and class” to the festival.

“I think a lot of kids don’t know her, but by the time they leave here, they know who she is,” he says. “I think she’s accomplishing a lot by doing this.”

Jett began her long and turbulent career at the age of 15 when she joined the Los Angeles-based all-girl band the Runaways as a guitarist and songwriter.

The Runaways played time-tested power-pop, but they raised eyebrows for their sexually charged songs and also for being young females in the male world of rock. Commercial success eluded them; they played their last show in 1978, when Jett was 18.

She quickly became involved in the budding punk scene at the time, traveling to England to work briefly with guitarist Steve Jones and drummer Paul Cook of the Sex Pistols, then producing the seminal punk album “(GI)” by the Germs.

Soon after, she met producer and songwriter Kenny Laguna, who had worked with the likes of Tommy James and the Shondells, and they formed an unlikely but lasting partnership.

Jett says Laguna’s pop sensibility helped temper her hard-rock instincts, but there’s another reason the two have remained close: Laguna treats Jett like an equal.

“He came to my defense early on, when nobody else was there to defend me,” she says.

“I think he was truly offended in his heart and soul by what he saw, people writing me off because I was just some little girl. And that still happens to some extent.”

Jett wound up with a string of Top 20 hits, including the Tommy James cover “Crimson and Clover,” “Do You Wanna Touch Me (Oh Yeah)” and “I Hate Myself for Loving You.”

Her charismatic presence made her a natural for MTV; in an era of dolled-up female singers such as Debbie Harry and Madonna, Jett stood out for her aggressive, masculine swagger.

There’s been plenty of speculation about her sexual orientation, and she likes to fan the flames. Her new album features a cover of the Replacements’ “Androgynous” and a cheeky version of Sweet’s ode to bisexuality, “A.C.D.C.”

Jett won’t publicly discuss her sexuality. “But I do it in my music, and I always have,” she says. “If you don’t know who I am from listening to my music, then you’re not going to figure it out from me talking to you, either.”

After the Warped Tour, Jett plans to embark on her own headlining tour in October with the Eagles of Death Metal tentatively slotted as support act.

Which brings up a question: Why, after all these years, is she still one of the few active, well-known female rock artists around?

“People will really cut down women – really get nasty – for no reason at all, just because you’re trying to play music,” explains Jett.

“Most women choose not to go that route, because that’s not the kind of life they want, sparring with people for the rest of their lives. But this is all that I’ve ever done. And it’s my job now to be the warrior, and to fight.”