Elliptic curve isogeny class with Cremona label 58482c (LMFDB label 58482.g)

• Label: 58482c
• Number of curves: $4$
• Conductor: $58482$
• CM: no
• Rank: $0$

Elliptic curves in class 58482c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
58482.g3	58482c1	\([1, -1, 0, -1692, -27656]\)	\(-140625/8\)	\(-30485730888\)	\([]\)	\(43092\)	\(0.76863\)	\(\Gamma_0(N)\)-optimal
58482.g4	58482c2	\([1, -1, 0, 9138, -54370]\)	\(3375/2\)	\(-50004220089042\)	\([]\)	\(129276\)	\(1.3179\)
58482.g2	58482c3	\([1, -1, 0, -34182, 4949812]\)	\(-1159088625/2097152\)	\(-7991651437903872\)	\([]\)	\(301644\)	\(1.7416\)
58482.g1	58482c4	\([1, -1, 0, -3499782, 2520929204]\)	\(-189613868625/128\)	\(-3200270085698688\)	\([]\)	\(904932\)	\(2.2909\)

Rank

The elliptic curves in class 58482c have rank \(0\).

Complex multiplication

The elliptic curves in class 58482c do not have complex multiplication.

Modular form 58482.2.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.

\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.