Elliptic curve isogeny class with Cremona label 65072e (LMFDB label 65072.h)

• Label: 65072e
• Number of curves: $1$
• Conductor: $65072$
• CM: no
• Rank: $1$

Rank

The elliptic curve 65072e1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(83\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 65072e do not have complex multiplication.

Modular form 65072.2.a.e

Elliptic curves in class 65072e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
65072.h1	65072e1	\([0, -1, 0, -163, 1058]\)	\(-256000/83\)	\(-156237872\)	\([]\)	\(12096\)	\(0.28487\)	\(\Gamma_0(N)\)-optimal