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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 5010a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5010.a2 | 5010a1 | \([1, 1, 0, -5367, -337131]\) | \(-17101922279625721/38553753600000\) | \(-38553753600000\) | \([2]\) | \(15120\) | \(1.2955\) | \(\Gamma_0(N)\)-optimal |
| 5010.a1 | 5010a2 | \([1, 1, 0, -112247, -14509419]\) | \(156406207396688718841/152178750000000\) | \(152178750000000\) | \([2]\) | \(30240\) | \(1.6421\) |
Rank
sage: E.rank()
The elliptic curves in class 5010a have rank \(0\).
Complex multiplication
The elliptic curves in class 5010a do not have complex multiplication.Modular form 5010.2.a.a
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.
