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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 325864t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 325864.t2 | 325864t1 | \([0, -1, 0, 2024836, -1176298252]\) | \(24226243449392/29774625727\) | \(-1128374576419511373568\) | \([2]\) | \(11827200\) | \(2.7257\) | \(\Gamma_0(N)\)-optimal |
| 325864.t1 | 325864t2 | \([0, -1, 0, -12057144, -11298425476]\) | \(1278763167594532/375974556419\) | \(56993513165688137206784\) | \([2]\) | \(23654400\) | \(3.0723\) |
Rank
sage: E.rank()
The elliptic curves in class 325864t have rank \(1\).
Complex multiplication
The elliptic curves in class 325864t do not have complex multiplication.Modular form 325864.2.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.
