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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 25872.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25872.t1 | 25872bu2 | \([0, -1, 0, -2791448, 1109780400]\) | \(14553591673375/5208653241\) | \(860929826351473815552\) | \([2]\) | \(1146880\) | \(2.7179\) | |
| 25872.t2 | 25872bu1 | \([0, -1, 0, 528792, 121676976]\) | \(98931640625/96059601\) | \(-15877535282506985472\) | \([2]\) | \(573440\) | \(2.3713\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25872.t have rank \(0\).
Complex multiplication
The elliptic curves in class 25872.t do not have complex multiplication.Modular form 25872.2.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 LMFDB 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 LMFDB labels.
