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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 66240g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66240.g4 | 66240g1 | \([0, 0, 0, -44268, 709808]\) | \(1355469437763/753664000\) | \(5334349381632000\) | \([2]\) | \(331776\) | \(1.7081\) | \(\Gamma_0(N)\)-optimal |
| 66240.g3 | 66240g2 | \([0, 0, 0, -535788, 150721712]\) | \(2403250125069123/4232000000\) | \(29953622016000000\) | \([2]\) | \(663552\) | \(2.0547\) | |
| 66240.g2 | 66240g3 | \([0, 0, 0, -2194668, -1251396432]\) | \(226568219476347/3893440\) | \(20089295213690880\) | \([2]\) | \(995328\) | \(2.2574\) | |
| 66240.g1 | 66240g4 | \([0, 0, 0, -2263788, -1168369488]\) | \(248656466619387/29607177800\) | \(152766534290610585600\) | \([2]\) | \(1990656\) | \(2.6040\) |
Rank
sage: E.rank()
The elliptic curves in class 66240g have rank \(1\).
Complex multiplication
The elliptic curves in class 66240g do not have complex multiplication.Modular form 66240.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
