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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 2496.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2496.s1 | 2496bb3 | \([0, 1, 0, -3329, 72831]\) | \(62275269892/39\) | \(2555904\) | \([2]\) | \(1024\) | \(0.54970\) | |
| 2496.s2 | 2496bb2 | \([0, 1, 0, -209, 1071]\) | \(61918288/1521\) | \(24920064\) | \([2, 2]\) | \(512\) | \(0.20313\) | |
| 2496.s3 | 2496bb1 | \([0, 1, 0, -29, -45]\) | \(2725888/1053\) | \(1078272\) | \([2]\) | \(256\) | \(-0.14345\) | \(\Gamma_0(N)\)-optimal |
| 2496.s4 | 2496bb4 | \([0, 1, 0, 31, 3615]\) | \(48668/85683\) | \(-5615321088\) | \([2]\) | \(1024\) | \(0.54970\) |
Rank
sage: E.rank()
The elliptic curves in class 2496.s have rank \(1\).
Complex multiplication
The elliptic curves in class 2496.s do not have complex multiplication.Modular form 2496.2.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.
