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.