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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 302016.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302016.g1 | 302016g2 | \([0, -1, 0, -1019465, 396508521]\) | \(16148234224576/1146717\) | \(8320938456010752\) | \([2]\) | \(5160960\) | \(2.1071\) | |
| 302016.g2 | 302016g1 | \([0, -1, 0, -67800, 5374206]\) | \(304006671424/66806883\) | \(7574557981079232\) | \([2]\) | \(2580480\) | \(1.7605\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 302016.g have rank \(0\).
Complex multiplication
The elliptic curves in class 302016.g do not have complex multiplication.Modular form 302016.2.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 LMFDB 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 LMFDB labels.
