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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 43120.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43120.g1 | 43120k2 | \([0, 1, 0, -13736, -614636]\) | \(1189646642/21175\) | \(5102013593600\) | \([2]\) | \(98304\) | \(1.2343\) | |
| 43120.g2 | 43120k1 | \([0, 1, 0, -16, -27420]\) | \(-4/2695\) | \(-324673592320\) | \([2]\) | \(49152\) | \(0.88772\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43120.g have rank \(1\).
Complex multiplication
The elliptic curves in class 43120.g do not have complex multiplication.Modular form 43120.2.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.
