Elliptic curve isogeny class with LMFDB label 10304.r (Cremona label 10304w)

• Label: 10304.r
• Number of curves: $4$
• Conductor: $10304$
• CM: no
• Rank: $1$

Elliptic curves in class 10304.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10304.r1	10304w3	\([0, 0, 0, -7916, -271024]\)	\(209267191953/55223\)	\(14476378112\)	\([2]\)	\(10240\)	\(0.93409\)
10304.r2	10304w2	\([0, 0, 0, -556, -3120]\)	\(72511713/25921\)	\(6795034624\)	\([2, 2]\)	\(5120\)	\(0.58751\)
10304.r3	10304w1	\([0, 0, 0, -236, 1360]\)	\(5545233/161\)	\(42205184\)	\([2]\)	\(2560\)	\(0.24094\)	\(\Gamma_0(N)\)-optimal
10304.r4	10304w4	\([0, 0, 0, 1684, -21936]\)	\(2014698447/1958887\)	\(-513510473728\)	\([2]\)	\(10240\)	\(0.93409\)

Rank

The elliptic curves in class 10304.r have rank \(1\).

Complex multiplication

The elliptic curves in class 10304.r do not have complex multiplication.

Modular form 10304.2.a.r

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.