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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 4056h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4056.s2 | 4056h1 | \([0, 1, 0, 789, 27522]\) | \(702464/4563\) | \(-352395671472\) | \([2]\) | \(8064\) | \(0.89743\) | \(\Gamma_0(N)\)-optimal |
| 4056.s1 | 4056h2 | \([0, 1, 0, -10196, 357072]\) | \(94875856/9477\) | \(11710379236608\) | \([2]\) | \(16128\) | \(1.2440\) |
Rank
sage: E.rank()
The elliptic curves in class 4056h have rank \(0\).
Complex multiplication
The elliptic curves in class 4056h do not have complex multiplication.Modular form 4056.2.a.h
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 Cremona 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 Cremona labels.
