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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 26010g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26010.f2 | 26010g1 | \([1, -1, 0, 647595, -457045259]\) | \(347428927/1244160\) | \(-107558331176007982080\) | \([2]\) | \(870400\) | \(2.5266\) | \(\Gamma_0(N)\)-optimal |
| 26010.f1 | 26010g2 | \([1, -1, 0, -6427125, -5464532075]\) | \(339630096833/47239200\) | \(4083855386839053069600\) | \([2]\) | \(1740800\) | \(2.8732\) |
Rank
sage: E.rank()
The elliptic curves in class 26010g have rank \(0\).
Complex multiplication
The elliptic curves in class 26010g do not have complex multiplication.Modular form 26010.2.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.
