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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 7225.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7225.g1 | 7225b3 | \([1, -1, 0, -655217, -203975184]\) | \(82483294977/17\) | \(6411541765625\) | \([2]\) | \(36864\) | \(1.8447\) | |
| 7225.g2 | 7225b2 | \([1, -1, 0, -41092, -3156309]\) | \(20346417/289\) | \(108996210015625\) | \([2, 2]\) | \(18432\) | \(1.4981\) | |
| 7225.g3 | 7225b4 | \([1, -1, 0, -4967, -8538934]\) | \(-35937/83521\) | \(-31499904694515625\) | \([2]\) | \(36864\) | \(1.8447\) | |
| 7225.g4 | 7225b1 | \([1, -1, 0, -4967, 58816]\) | \(35937/17\) | \(6411541765625\) | \([2]\) | \(9216\) | \(1.1515\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7225.g have rank \(1\).
Complex multiplication
The elliptic curves in class 7225.g do not have complex multiplication.Modular form 7225.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
