Elliptic curve isogeny class with Cremona label 1058c (LMFDB label 1058.a)

• Label: 1058c
• Number of curves: $2$
• Conductor: $1058$
• CM: no
• Rank: $2$

Elliptic curves in class 1058c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1058.a2	1058c1	$[1, 0, 1, 0, 2]$	$23/4$	$-2116$	$[]$	$80$	$-0.68263$	$\Gamma_0(N)$-optimal
1058.a1	1058c2	$[1, 0, 1, -115, 462]$	$-313994137/64$	$-33856$	$[]$	$240$	$-0.13332$

Rank

The elliptic curves in class 1058c have rank $2$.

Complex multiplication

The elliptic curves in class 1058c do not have complex multiplication.

Modular form 1058.2.a.c

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.

$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.