Elliptic curve isogeny class with LMFDB label 475600.h (Cremona label 475600h)

• Label: 475600.h
• Number of curves: $2$
• Conductor: $475600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 475600.h have rank $1$.

Complex multiplication

The elliptic curves in class 475600.h do not have complex multiplication.

Modular form 475600.2.a.h

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.

Elliptic curves in class 475600.h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
475600.h1	475600h2	$[0, 1, 0, -2139328, 1814387508]$	$-10574408522150085865/7779603246481408$	$-796631372439696179200$	$[]$	$22021632$	$2.7100$	$\Gamma_0(N)$-optimal^*
475600.h2	475600h1	$[0, 1, 0, 215472, -38369132]$	$10804241130540935/12486531154432$	$-1278620790213836800$	$[]$	$7340544$	$2.1607$	$\Gamma_0(N)$-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 475600.h1.