Elliptic curve isogeny class with Cremona label 493680et (LMFDB label 493680.et)

• Label: 493680et
• Number of curves: $4$
• Conductor: $493680$
• CM: no
• Rank: $0$

Elliptic curves in class 493680et

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
493680.et3	493680et1	$[0, 1, 0, -115111, 12285260]$	$5951163357184/1129312125$	$32010325079634000$	$[2]$	$4423680$	$1.8846$	$\Gamma_0(N)$-optimal
493680.et2	493680et2	$[0, 1, 0, -556156, -148607956]$	$41948679809104/3291890625$	$1492936972164000000$	$[2, 2]$	$8847360$	$2.2312$
493680.et4	493680et3	$[0, 1, 0, 554624, -667120060]$	$10400706415004/112060546875$	$-203286624750000000000$	$[2]$	$17694720$	$2.5778$
493680.et1	493680et4	$[0, 1, 0, -8723656, -9920204956]$	$40472803590982276/281883375$	$511358559947136000$	$[2]$	$17694720$	$2.5778$

Rank

The elliptic curves in class 493680et have rank $0$.

Complex multiplication

The elliptic curves in class 493680et do not have complex multiplication.

Modular form 493680.2.a.et

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.