Elliptic curve isogeny class with LMFDB label 504.b (Cremona label 504f)

• Label: 504.b
• Number of curves: $4$
• Conductor: $504$
• CM: no
• Rank: $1$

Elliptic curves in class 504.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
504.b1	504f3	\([0, 0, 0, -1371, -19514]\)	\(381775972/567\)	\(423263232\)	\([2]\)	\(256\)	\(0.55626\)
504.b2	504f2	\([0, 0, 0, -111, -110]\)	\(810448/441\)	\(82301184\)	\([2, 2]\)	\(128\)	\(0.20969\)
504.b3	504f1	\([0, 0, 0, -66, 205]\)	\(2725888/21\)	\(244944\)	\([4]\)	\(64\)	\(-0.13688\)	\(\Gamma_0(N)\)-optimal
504.b4	504f4	\([0, 0, 0, 429, -866]\)	\(11696828/7203\)	\(-5377010688\)	\([2]\)	\(256\)	\(0.55626\)

Rank

The elliptic curves in class 504.b have rank \(1\).

Complex multiplication

The elliptic curves in class 504.b do not have complex multiplication.

Modular form 504.2.a.b

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.