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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 51425g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51425.w1 | 51425g1 | \([0, -1, 1, -39794883, -96611732207]\) | \(-251784668965666816/353546875\) | \(-9786403990966796875\) | \([]\) | \(4216320\) | \(2.9163\) | \(\Gamma_0(N)\)-optimal |
| 51425.w2 | 51425g2 | \([0, -1, 1, -29207383, -149149554082]\) | \(-99546392709922816/289614925147075\) | \(-8016726662632458344921875\) | \([]\) | \(12648960\) | \(3.4656\) |
Rank
sage: E.rank()
The elliptic curves in class 51425g have rank \(0\).
Complex multiplication
The elliptic curves in class 51425g do not have complex multiplication.Modular form 51425.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
