Elliptic curve isogeny class with LMFDB label 960.m (Cremona label 960h)

• Label: 960.m
• Number of curves: $4$
• Conductor: $960$
• CM: no
• Rank: $1$

Elliptic curves in class 960.m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
960.m1	960h3	$[0, 1, 0, -1985, -19617]$	$26410345352/10546875$	$345600000000$	$[2]$	$1536$	$0.91221$
960.m2	960h2	$[0, 1, 0, -905, 9975]$	$20034997696/455625$	$1866240000$	$[2, 2]$	$768$	$0.56564$
960.m3	960h1	$[0, 1, 0, -900, 10098]$	$1261112198464/675$	$43200$	$[2]$	$384$	$0.21907$	$\Gamma_0(N)$-optimal
960.m4	960h4	$[0, 1, 0, 95, 31775]$	$2863288/13286025$	$-435356467200$	$[4]$	$1536$	$0.91221$

Rank

The elliptic curves in class 960.m have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 - T$
$5$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 4 T + 7 T^{2}$	1.7.e
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 + 6 T + 13 T^{2}$	1.13.g
$17$	$1 - 2 T + 17 T^{2}$	1.17.ac
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 + 23 T^{2}$	1.23.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 960.m do not have complex multiplication.

Modular form 960.2.a.m

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.