Elliptic curve isogeny class with LMFDB label 46410.p (Cremona label 46410n)

• Label: 46410.p
• Number of curves: $4$
• Conductor: $46410$
• CM: no
• Rank: $1$

Elliptic curves in class 46410.p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
46410.p1	46410n4	$[1, 1, 0, -740012, -245331216]$	$44816807438220995641801/9512718589920$	$9512718589920$	$[2]$	$491520$	$1.8758$
46410.p2	46410n3	$[1, 1, 0, -90092, 4453296]$	$80870462846141298121/38087635627860000$	$38087635627860000$	$[2]$	$491520$	$1.8758$
46410.p3	46410n2	$[1, 1, 0, -46412, -3819696]$	$11056793118237203401/159353257190400$	$159353257190400$	$[2, 2]$	$245760$	$1.5292$
46410.p4	46410n1	$[1, 1, 0, -332, -160944]$	$-4066120948681/11168482590720$	$-11168482590720$	$[2]$	$122880$	$1.1826$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 46410.p have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1 + T$
$5$	$1 - T$
$7$	$1 - T$
$13$	$1 + T$
$17$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 + 11 T^{2}$	1.11.a
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 46410.p do not have complex multiplication.

Modular form 46410.2.a.p

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.