Elliptic curve isogeny class with LMFDB label 236992.b (Cremona label 236992b)

• Label: 236992.b
• Number of curves: $1$
• Conductor: $236992$
• CM: no
• Rank: $2$

Rank

The elliptic curve 236992.b1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1 + T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 236992.b do not have complex multiplication.

Modular form 236992.2.a.b

Isogeny graph

Elliptic curves in class 236992.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
236992.b1	236992b1	\([0, 0, 0, -460, 4048]\)	\(-621000/49\)	\(-849379328\)	\([]\)	\(205824\)	\(0.46037\)	\(\Gamma_0(N)\)-optimal