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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 32064g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32064.b2 | 32064g1 | \([0, -1, 0, -289, -7775]\) | \(-10218313/96192\) | \(-25216155648\) | \([2]\) | \(27648\) | \(0.67830\) | \(\Gamma_0(N)\)-optimal |
| 32064.b1 | 32064g2 | \([0, -1, 0, -7969, -270431]\) | \(213525509833/669336\) | \(175462416384\) | \([2]\) | \(55296\) | \(1.0249\) |
Rank
sage: E.rank()
The elliptic curves in class 32064g have rank \(0\).
Complex multiplication
The elliptic curves in class 32064g do not have complex multiplication.Modular form 32064.2.a.g
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.
