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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 2520.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2520.s1 | 2520i3 | \([0, 0, 0, -5907, -174386]\) | \(15267472418/36015\) | \(53770106880\) | \([2]\) | \(2048\) | \(0.93893\) | |
| 2520.s2 | 2520i2 | \([0, 0, 0, -507, -506]\) | \(19307236/11025\) | \(8230118400\) | \([2, 2]\) | \(1024\) | \(0.59236\) | |
| 2520.s3 | 2520i1 | \([0, 0, 0, -327, 2266]\) | \(20720464/105\) | \(19595520\) | \([2]\) | \(512\) | \(0.24578\) | \(\Gamma_0(N)\)-optimal |
| 2520.s4 | 2520i4 | \([0, 0, 0, 2013, -4034]\) | \(604223422/354375\) | \(-529079040000\) | \([2]\) | \(2048\) | \(0.93893\) |
Rank
sage: E.rank()
The elliptic curves in class 2520.s have rank \(0\).
Complex multiplication
The elliptic curves in class 2520.s do not have complex multiplication.Modular form 2520.2.a.s
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().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
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
