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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 60840.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60840.g1 | 60840bg2 | \([0, 0, 0, -57498363, 165778690662]\) | \(216092050322508/3016755625\) | \(293488774058107854720000\) | \([2]\) | \(9289728\) | \(3.3083\) | |
| 60840.g2 | 60840bg1 | \([0, 0, 0, -460863, 6952068162]\) | \(-445090032/858203125\) | \(-20872836115875900000000\) | \([2]\) | \(4644864\) | \(2.9617\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 60840.g have rank \(0\).
Complex multiplication
The elliptic curves in class 60840.g do not have complex multiplication.Modular form 60840.2.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.
