Elliptic curve isogeny class with LMFDB label 430950.cm (Cremona label 430950cm)

• Label: 430950.cm
• Number of curves: $4$
• Conductor: $430950$
• CM: no
• Rank: $1$

Elliptic curves in class 430950.cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
430950.cm1	430950cm4	\([1, 0, 1, -31254526, -66835007302]\)	\(44769506062996441/323730468750\)	\(24415392814636230468750\)	\([2]\)	\(86704128\)	\(3.1275\)
430950.cm2	430950cm2	\([1, 0, 1, -3242776, 505239698]\)	\(50002789171321/27473062500\)	\(2071987895821289062500\)	\([2, 2]\)	\(43352064\)	\(2.7809\)
430950.cm3	430950cm1	\([1, 0, 1, -2482276, 1503015698]\)	\(22428153804601/35802000\)	\(2700147122156250000\)	\([2]\)	\(21676032\)	\(2.4343\)	\(\Gamma_0(N)\)-optimal^*
430950.cm4	430950cm3	\([1, 0, 1, 12600974, 3990864698]\)	\(2933972022568679/1789082460750\)	\(-134930614426410105468750\)	\([2]\)	\(86704128\)	\(3.1275\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 430950.cm1.

Rank

The elliptic curves in class 430950.cm have rank \(1\).

Complex multiplication

The elliptic curves in class 430950.cm do not have complex multiplication.

Modular form 430950.2.a.cm

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.