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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 11913d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11913.e2 | 11913d1 | \([0, -1, 1, -131163, 19754264]\) | \(-5304438784000/497763387\) | \(-23417717070958947\) | \([]\) | \(64800\) | \(1.8831\) | \(\Gamma_0(N)\)-optimal |
| 11913.e1 | 11913d2 | \([0, -1, 1, -10852863, 13765080881]\) | \(-3004935183806464000/2037123\) | \(-95838246240363\) | \([]\) | \(194400\) | \(2.4324\) |
Rank
sage: E.rank()
The elliptic curves in class 11913d have rank \(1\).
Complex multiplication
The elliptic curves in class 11913d do not have complex multiplication.Modular form 11913.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
