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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 12688g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12688.f2 | 12688g1 | \([0, 1, 0, 256080, -661017004]\) | \(453407867428435919/46358174206263296\) | \(-189883081548854460416\) | \([]\) | \(225600\) | \(2.5705\) | \(\Gamma_0(N)\)-optimal |
| 12688.f1 | 12688g2 | \([0, 1, 0, -55887280, 169315451476]\) | \(-4713056995643685597046321/296750651251759162016\) | \(-1215490667527205527617536\) | \([]\) | \(1128000\) | \(3.3752\) |
Rank
sage: E.rank()
The elliptic curves in class 12688g have rank \(0\).
Complex multiplication
The elliptic curves in class 12688g do not have complex multiplication.Modular form 12688.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
