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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 485520t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485520.t2 | 485520t1 | \([0, -1, 0, -183156736, 1460185753936]\) | \(-27491530342319084164/21352892495484375\) | \(-527776681942360360944000000\) | \([2]\) | \(185794560\) | \(3.8263\) | \(\Gamma_0(N)\)-optimal* |
485520.t1 | 485520t2 | \([0, -1, 0, -3343371736, 74392891609936]\) | \(83609231549925663172082/22317062975463375\) | \(1103215917972669483080448000\) | \([2]\) | \(371589120\) | \(4.1729\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485520t have rank \(1\).
Complex multiplication
The elliptic curves in class 485520t do not have complex multiplication.Modular form 485520.2.a.t
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.