Elliptic curve isogeny class with LMFDB label 50.a (Cremona label 50a)

• Label: 50.a
• Number of curves: $4$
• Conductor: $50$
• CM: no
• Rank: $0$

Elliptic curves in class 50.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
50.a1	50a2	$[1, 0, 1, -126, -552]$	$-349938025/8$	$-5000$	$[]$	$6$	$-0.17679$
50.a2	50a3	$[1, 0, 1, -76, 298]$	$-121945/32$	$-12500000$	$[3]$	$10$	$0.078619$
50.a3	50a1	$[1, 0, 1, -1, -2]$	$-25/2$	$-1250$	$[3]$	$2$	$-0.72610$	$\Gamma_0(N)$-optimal
50.a4	50a4	$[1, 0, 1, 549, -2202]$	$46969655/32768$	$-12800000000$	$[]$	$30$	$0.62793$

Rank

The elliptic curves in class 50.a have rank $0$.

Complex multiplication

The elliptic curves in class 50.a do not have complex multiplication.

Modular form 50.2.a.a

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.

$\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.