Elliptic curve isogeny class with LMFDB label 46410.cn (Cremona label 46410cm)

• Label: 46410.cn
• Number of curves: $6$
• Conductor: $46410$
• CM: no
• Rank: $0$

Elliptic curves in class 46410.cn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
46410.cn1	46410cm6	$[1, 0, 0, -73322765620, -7595474963359738]$	$43595355616903186726969048523604598081/306218213075771927833557128906250$	$306218213075771927833557128906250$	$[2]$	$270532608$	$5.0663$
46410.cn2	46410cm4	$[1, 0, 0, -7562905090, 54672107453600]$	$47839833887939781795850621588688161/26393794292755443609008789062500$	$26393794292755443609008789062500$	$[2, 2]$	$135266304$	$4.7198$
46410.cn3	46410cm2	$[1, 0, 0, -5766634510, 168310291664372]$	$21207574048850823872792738495132641/34982717474287728110306250000$	$34982717474287728110306250000$	$[2, 4]$	$67633152$	$4.3732$
46410.cn4	46410cm1	$[1, 0, 0, -5764349630, 168450516120900]$	$21182375175311718755156119308023521/57778579333189522080000$	$57778579333189522080000$	$[8]$	$33816576$	$4.0266$	$\Gamma_0(N)$-optimal
46410.cn5	46410cm3	$[1, 0, 0, -4006922010, 272974119796872]$	$-7114696532582636527413245800532641/28073201392582203302585928742500$	$-28073201392582203302585928742500$	$[4]$	$135266304$	$4.7198$
46410.cn6	46410cm5	$[1, 0, 0, 29456626160, 431982573859850]$	$2826654455041045345083039379223811839/1716409549902715755405793403906250$	$-1716409549902715755405793403906250$	$[2]$	$270532608$	$5.0663$

Rank

The elliptic curves in class 46410.cn have rank $0$.

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 $\mathbb{F}_p$
$11$	$1 - 4 T + 11 T^{2}$	1.11.ae
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 - 6 T + 29 T^{2}$	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 46410.2.a.cn

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.

$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.