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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 76230e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76230.be1 | 76230e1 | \([1, -1, 0, -31785, 2188665]\) | \(74246873427/16940\) | \(810276570180\) | \([2]\) | \(245760\) | \(1.2768\) | \(\Gamma_0(N)\)-optimal |
| 76230.be2 | 76230e2 | \([1, -1, 0, -28155, 2704851]\) | \(-51603494067/35870450\) | \(-1715760637356150\) | \([2]\) | \(491520\) | \(1.6234\) |
Rank
sage: E.rank()
The elliptic curves in class 76230e have rank \(1\).
Complex multiplication
The elliptic curves in class 76230e do not have complex multiplication.Modular form 76230.2.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 Cremona 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 Cremona labels.
