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SageMath
sage: E = EllipticCurve("t1")
sage: E.isogeny_class()
Elliptic curves in class 424830.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 424830.t1 | 424830t1 | \([1, 1, 0, -33198, 2377908]\) | \(-5831629329001/186624000\) | \(-129496340736000\) | \([]\) | \(2309472\) | \(1.4837\) | \(\Gamma_0(N)\)-optimal |
| 424830.t2 | 424830t2 | \([1, 1, 0, 154227, 8862813]\) | \(584669638645799/386547056640\) | \(-268220750584872960\) | \([]\) | \(6928416\) | \(2.0330\) |
Rank
sage: E.rank()
The elliptic curves in class 424830.t have rank \(1\).
Complex multiplication
The elliptic curves in class 424830.t do not have complex multiplication.Modular form 424830.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
