Elliptic curve isogeny class with LMFDB label 388080.r (Cremona label 388080r)

• Label: 388080.r
• Number of curves: $1$
• Conductor: $388080$
• CM: no
• Rank: $1$

Rank

The elliptic curve 388080.r1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 388080.r do not have complex multiplication.

Modular form 388080.2.a.r

Elliptic curves in class 388080.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
388080.r1	388080r1	\([0, 0, 0, -5119241043, 155869767626258]\)	\(-861923363555648023441/110929177533556800\)	\(-1909490884099695367739257651200\)	\([]\)	\(553512960\)	\(4.5439\)	\(\Gamma_0(N)\)-optimal