Elliptic curve isogeny class with Cremona label 318402r (LMFDB label 318402.r)

• Label: 318402r
• Number of curves: $4$
• Conductor: $318402$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 318402r have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 318402r do not have complex multiplication.

Modular form 318402.2.a.r

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 318402r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
318402.r3	318402r1	\([1, -1, 0, -25714278, 29371676004]\)	\(466025146777/177366672\)	\(715664362382282350153872\)	\([2]\)	\(44236800\)	\(3.2766\)	\(\Gamma_0(N)\)-optimal
318402.r2	318402r2	\([1, -1, 0, -181731258, -921988664640]\)	\(164503536215257/4178071044\)	\(16858277352647946993165444\)	\([2, 2]\)	\(88473600\)	\(3.6232\)
318402.r4	318402r3	\([1, -1, 0, 30006072, -2942598004830]\)	\(740480746823/927484650666\)	\(-3742347441340257977441452266\)	\([2]\)	\(176947200\)	\(3.9698\)
318402.r1	318402r4	\([1, -1, 0, -2889740268, -59790313329426]\)	\(661397832743623417/443352042\)	\(1788900095328015539251242\)	\([2]\)	\(176947200\)	\(3.9698\)