Elliptic curve isogeny class with Cremona label 438702a (LMFDB label 438702.a)

• Label: 438702a
• Number of curves: $2$
• Conductor: $438702$
• CM: no
• Rank: $1$

Elliptic curves in class 438702a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
438702.a2	438702a1	$[1, 1, 0, 1361618, -723944780]$	$11566328890520951/16088147361792$	$-388328767027422363648$	$[2]$	$39813120$	$2.6364$	$\Gamma_0(N)$-optimal^*
438702.a1	438702a2	$[1, 1, 0, -8626222, -7166101580]$	$2940980566145956489/783792101714688$	$18918835936793299913472$	$[2]$	$79626240$	$2.9829$	$\Gamma_0(N)$-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 438702a1.

Rank

The elliptic curves in class 438702a have rank $1$.

Complex multiplication

The elliptic curves in class 438702a do not have complex multiplication.

Modular form 438702.2.a.a

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.