Elliptic curve isogeny class with LMFDB label 310464.ey (Cremona label 310464ey)

• Label: 310464.ey
• Number of curves: $4$
• Conductor: $310464$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 310464.ey have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 310464.ey do not have complex multiplication.

Modular form 310464.2.a.ey

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 310464.ey

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
310464.ey1	310464ey3	\([0, 0, 0, -145739916, 677198252304]\)	\(15226621995131793/2324168\)	\(52254441186873311232\)	\([2]\)	\(28311552\)	\(3.1892\)
310464.ey2	310464ey4	\([0, 0, 0, -17038476, -10395287280]\)	\(24331017010833/12004097336\)	\(269889008989674839998464\)	\([2]\)	\(28311552\)	\(3.1892\)
310464.ey3	310464ey2	\([0, 0, 0, -9135756, 10515309840]\)	\(3750606459153/45914176\)	\(1032291817732517658624\)	\([2, 2]\)	\(14155776\)	\(2.8426\)
310464.ey4	310464ey1	\([0, 0, 0, -104076, 425116944]\)	\(-5545233/3469312\)	\(-78000798506353164288\)	\([2]\)	\(7077888\)	\(2.4960\)	\(\Gamma_0(N)\)-optimal