Elliptic curve isogeny class with LMFDB label 355008.r (Cremona label 355008r)

• Label: 355008.r
• Number of curves: $1$
• Conductor: $355008$
• CM: no
• Rank: $2$

Rank

The elliptic curve 355008.r1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(43\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 355008.r do not have complex multiplication.

Modular form 355008.2.a.r

Isogeny graph

Elliptic curves in class 355008.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
355008.r1	355008r1	\([0, -1, 0, -1089, 14913]\)	\(-294937/18\)	\(-8724676608\)	\([]\)	\(258048\)	\(0.66220\)	\(\Gamma_0(N)\)-optimal