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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 350064g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350064.g1 | 350064g1 | \([0, 0, 0, -797052, -273890905]\) | \(4801049335176577024/6222978333\) | \(72584819276112\) | \([2]\) | \(4571136\) | \(1.9367\) | \(\Gamma_0(N)\)-optimal |
| 350064.g2 | 350064g2 | \([0, 0, 0, -790167, -278854990]\) | \(-292356586786125904/10812404517057\) | \(-2017854180591245568\) | \([2]\) | \(9142272\) | \(2.2833\) |
Rank
sage: E.rank()
The elliptic curves in class 350064g have rank \(1\).
Complex multiplication
The elliptic curves in class 350064g do not have complex multiplication.Modular form 350064.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
