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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 77616.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77616.u1 | 77616fr2 | \([0, 0, 0, -34104, 2438044]\) | \(-199794688/1331\) | \(-29223605005056\) | \([]\) | \(259200\) | \(1.4193\) | |
| 77616.u2 | 77616fr1 | \([0, 0, 0, 1176, 17836]\) | \(8192/11\) | \(-241517396736\) | \([]\) | \(86400\) | \(0.86997\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 77616.u have rank \(0\).
Complex multiplication
The elliptic curves in class 77616.u do not have complex multiplication.Modular form 77616.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
