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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 115920cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.n1 | 115920cc1 | \([0, 0, 0, -20403, 1100402]\) | \(8493409990827/185150000\) | \(20476108800000\) | \([2]\) | \(245760\) | \(1.3425\) | \(\Gamma_0(N)\)-optimal |
| 115920.n2 | 115920cc2 | \([0, 0, 0, 1677, 3356978]\) | \(4716275733/44023437500\) | \(-4868640000000000\) | \([2]\) | \(491520\) | \(1.6890\) |
Rank
sage: E.rank()
The elliptic curves in class 115920cc have rank \(1\).
Complex multiplication
The elliptic curves in class 115920cc do not have complex multiplication.Modular form 115920.2.a.cc
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.
