Elliptic curve isogeny class with LMFDB label 456475.k (Cremona label 456475k)

• Label: 456475.k
• Number of curves: $2$
• Conductor: $456475$
• CM: no
• Rank: $0$

Elliptic curves in class 456475.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
456475.k1	456475k2	$[1, -1, 0, -593117, -171499084]$	$13312053/361$	$625759431330078125$	$[2]$	$4838400$	$2.1951$	$\Gamma_0(N)$-optimal^*
456475.k2	456475k1	$[1, -1, 0, 7508, -8729709]$	$27/19$	$-32934706912109375$	$[2]$	$2419200$	$1.8485$	$\Gamma_0(N)$-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 456475.k1.

Rank

The elliptic curves in class 456475.k have rank $0$.

Complex multiplication

The elliptic curves in class 456475.k do not have complex multiplication.

Modular form 456475.2.a.k

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.