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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 53816.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53816.e1 | 53816e2 | \([0, 0, 0, -133579, 18410838]\) | \(290046852/6727\) | \(6113522956377088\) | \([2]\) | \(307200\) | \(1.8151\) | |
| 53816.e2 | 53816e1 | \([0, 0, 0, 961, 893730]\) | \(432/1519\) | \(-345118231408384\) | \([2]\) | \(153600\) | \(1.4685\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53816.e have rank \(0\).
Complex multiplication
The elliptic curves in class 53816.e do not have complex multiplication.Modular form 53816.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
