Elliptic curve isogeny class with Cremona label 103428r (LMFDB label 103428.s)

• Label: 103428r
• Number of curves: $4$
• Conductor: $103428$
• CM: no
• Rank: $0$

Elliptic curves in class 103428r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
103428.s2	103428r1	$[0, 0, 0, -4796220, -4042890839]$	$216727177216000/2738853$	$154197150496738128$	$[2]$	$1935360$	$2.4444$	$\Gamma_0(N)$-optimal
103428.s3	103428r2	$[0, 0, 0, -4666935, -4271130578]$	$-12479332642000/1526829993$	$-1375366019065964460288$	$[2]$	$3870720$	$2.7909$
103428.s1	103428r3	$[0, 0, 0, -7534020, 1074440653]$	$840033089536000/477272151837$	$26870374505207815023312$	$[2]$	$5806080$	$2.9937$
103428.s4	103428r4	$[0, 0, 0, 29829345, 8554586326]$	$3258571509326000/1920843121977$	$-1730292416336980668287232$	$[2]$	$11612160$	$3.3402$

Rank

The elliptic curves in class 103428r have rank $0$.

Complex multiplication

The elliptic curves in class 103428r do not have complex multiplication.

Modular form 103428.2.a.r

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.

$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.