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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 450528.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 450528.u1 | 450528u1 | \([0, -1, 0, -1047742, 413018188]\) | \(42246001231552/14414517\) | \(43401193693086528\) | \([2]\) | \(5474304\) | \(2.1640\) | \(\Gamma_0(N)\)-optimal |
| 450528.u2 | 450528u2 | \([0, -1, 0, -901537, 532233745]\) | \(-420526439488/390971529\) | \(-75340185713549512704\) | \([2]\) | \(10948608\) | \(2.5106\) |
Rank
sage: E.rank()
The elliptic curves in class 450528.u have rank \(0\).
Complex multiplication
The elliptic curves in class 450528.u do not have complex multiplication.Modular form 450528.2.a.u
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.
