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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 242550.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.t1 | 242550t3 | \([1, -1, 0, -13374657, 18830195901]\) | \(-24680042791780949/369098752\) | \(-3957021028122624000\) | \([]\) | \(11880000\) | \(2.7054\) | |
| 242550.t2 | 242550t1 | \([1, -1, 0, -12357, -526149]\) | \(-19465109/22\) | \(-235856832750\) | \([]\) | \(475200\) | \(1.0960\) | \(\Gamma_0(N)\)-optimal |
| 242550.t3 | 242550t2 | \([1, -1, 0, 86868, 5526576]\) | \(6761990971/5153632\) | \(-55250878212684000\) | \([]\) | \(2376000\) | \(1.9007\) |
Rank
sage: E.rank()
The elliptic curves in class 242550.t have rank \(0\).
Complex multiplication
The elliptic curves in class 242550.t do not have complex multiplication.Modular form 242550.2.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.
\(\left(\begin{array}{rrr} 1 & 25 & 5 \\ 25 & 1 & 5 \\ 5 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
