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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 132278.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 132278.g1 | 132278b3 | \([1, 0, 0, -297698, 502871108]\) | \(-69173457625/2550136832\) | \(-107566132431329165312\) | \([]\) | \(3673836\) | \(2.5239\) | |
| 132278.g2 | 132278b1 | \([1, 0, 0, -54028, -4839704]\) | \(-413493625/152\) | \(-6411441113432\) | \([]\) | \(408204\) | \(1.4253\) | \(\Gamma_0(N)\)-optimal |
| 132278.g3 | 132278b2 | \([1, 0, 0, 32997, -18370351]\) | \(94196375/3511808\) | \(-148129935484732928\) | \([]\) | \(1224612\) | \(1.9746\) |
Rank
sage: E.rank()
The elliptic curves in class 132278.g have rank \(0\).
Complex multiplication
The elliptic curves in class 132278.g do not have complex multiplication.Modular form 132278.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
