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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 350064r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350064.r1 | 350064r1 | \([0, 0, 0, -2200851, -684712494]\) | \(14623266529962819/5950368579584\) | \(479728045063994867712\) | \([2]\) | \(11206656\) | \(2.6660\) | \(\Gamma_0(N)\)-optimal |
| 350064.r2 | 350064r2 | \([0, 0, 0, 7199469, -4988178990]\) | \(511886728354194621/429557271832832\) | \(-34631580800965149720576\) | \([2]\) | \(22413312\) | \(3.0126\) |
Rank
sage: E.rank()
The elliptic curves in class 350064r have rank \(0\).
Complex multiplication
The elliptic curves in class 350064r do not have complex multiplication.Modular form 350064.2.a.r
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.
