Elliptic curve isogeny class with LMFDB label 132496.e (Cremona label 132496dg)

• Label: 132496.e
• Number of curves: $1$
• Conductor: $132496$
• CM: no
• Rank: $1$

Rank

The elliptic curve 132496.e1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 132496.e do not have complex multiplication.

Modular form 132496.2.a.e

Elliptic curves in class 132496.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
132496.e1	132496dg1	\([0, 0, 0, -57967, 5274997]\)	\(48384\)	\(445209493600144\)	\([]\)	\(774144\)	\(1.6011\)	\(\Gamma_0(N)\)-optimal