Elliptic curve isogeny class with LMFDB label 5415.b (Cremona label 5415b)

• Label: 5415.b
• Number of curves: $1$
• Conductor: $5415$
• CM: no
• Rank: $1$

Rank

The elliptic curve 5415.b1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 + T\)
\(5\)	\(1 + T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5415.b do not have complex multiplication.

Modular form 5415.2.a.b

Isogeny graph

Elliptic curves in class 5415.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5415.b1	5415b1	\([0, -1, 1, -13116, 396722]\)	\(1914902401024/597871125\)	\(77915162881125\)	\([]\)	\(21168\)	\(1.3699\)	\(\Gamma_0(N)\)-optimal