Elliptic curve isogeny class with LMFDB label 438080.z (Cremona label 438080z)

• Label: 438080.z
• Number of curves: $2$
• Conductor: $438080$
• CM: no
• Rank: $1$

Elliptic curves in class 438080.z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
438080.z1	438080z2	$[0, -1, 0, -65828821, -205553835379]$	$750484394082304/578125$	$24302560546048000000$	$[]$	$18911232$	$3.0276$
438080.z2	438080z1	$[0, -1, 0, -992981, -147410675]$	$2575826944/1266325$	$53232328620063539200$	$[]$	$6303744$	$2.4783$	$\Gamma_0(N)$-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 438080.z1.

Rank

The elliptic curves in class 438080.z have rank $1$.

Complex multiplication

The elliptic curves in class 438080.z do not have complex multiplication.

Modular form 438080.2.a.z

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.

$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.