Elliptic curve isogeny class with Cremona label 76296p (LMFDB label 76296.e)

• Label: 76296p
• Number of curves: $1$
• Conductor: $76296$
• CM: no
• Rank: $1$

Rank

The elliptic curve 76296p1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 76296p do not have complex multiplication.

Modular form 76296.2.a.p

Elliptic curves in class 76296p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
76296.e1	76296p1	\([0, -1, 0, 8319, 306549]\)	\(860492463104/1056655611\)	\(-78175608724224\)	\([]\)	\(230400\)	\(1.3519\)	\(\Gamma_0(N)\)-optimal