Elliptic curve isogeny class with Cremona label 317400cs (LMFDB label 317400.cs)

• Label: 317400cs
• Number of curves: $2$
• Conductor: $317400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 317400cs have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 317400cs do not have complex multiplication.

Modular form 317400.2.a.cs

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 317400cs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
317400.cs2	317400cs1	\([0, 1, 0, -850808, 427701888]\)	\(-28756228/16767\)	\(-39713884013808000000\)	\([2]\)	\(6488064\)	\(2.4634\)	\(\Gamma_0(N)\)-optimal
317400.cs1	317400cs2	\([0, 1, 0, -15133808, 22652049888]\)	\(80919167474/14283\)	\(67660691282784000000\)	\([2]\)	\(12976128\)	\(2.8099\)