Elliptic curve isogeny class with Cremona label 5070q (LMFDB label 5070.s)

• Label: 5070q
• Number of curves: $4$
• Conductor: $5070$
• CM: no
• Rank: $1$

Elliptic curves in class 5070q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5070.s3	5070q1	$[1, 1, 1, -2285, 39827]$	$273359449/9360$	$45178932240$	$[4]$	$5376$	$0.81636$	$\Gamma_0(N)$-optimal
5070.s2	5070q2	$[1, 1, 1, -5665, -110245]$	$4165509529/1368900$	$6607418840100$	$[2, 2]$	$10752$	$1.1629$
5070.s1	5070q3	$[1, 1, 1, -81715, -9023305]$	$12501706118329/2570490$	$12407264266410$	$[2]$	$21504$	$1.5095$
5070.s4	5070q4	$[1, 1, 1, 16305, -734193]$	$99317171591/106616250$	$-514616275046250$	$[2]$	$21504$	$1.5095$

Rank

The elliptic curves in class 5070q have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 - T$
$3$	$1 + T$
$5$	$1 - T$
$13$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 3 T + 7 T^{2}$	1.7.d
$11$	$1 - T + 11 T^{2}$	1.11.ab
$17$	$1 + 17 T^{2}$	1.17.a
$19$	$1 + 5 T + 19 T^{2}$	1.19.f
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5070q do not have complex multiplication.

Modular form 5070.2.a.q

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.