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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 57330a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57330.p2 | 57330a1 | \([1, -1, 0, 64230, -7415500]\) | \(9225324907317/12784844800\) | \(-40611353558630400\) | \([2]\) | \(516096\) | \(1.8726\) | \(\Gamma_0(N)\)-optimal |
| 57330.p1 | 57330a2 | \([1, -1, 0, -406170, -72989260]\) | \(2332898469575883/623520876160\) | \(1980628404102391680\) | \([2]\) | \(1032192\) | \(2.2191\) |
Rank
sage: E.rank()
The elliptic curves in class 57330a have rank \(0\).
Complex multiplication
The elliptic curves in class 57330a do not have complex multiplication.Modular form 57330.2.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.
