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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 86640cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 86640.h2 | 86640cc1 | \([0, -1, 0, -569056, 181477120]\) | \(-105756712489/12476160\) | \(-2404155140902748160\) | \([2]\) | \(1658880\) | \(2.2628\) | \(\Gamma_0(N)\)-optimal |
| 86640.h1 | 86640cc2 | \([0, -1, 0, -9348576, 11004869376]\) | \(468898230633769/5540400\) | \(1067634684282470400\) | \([2]\) | \(3317760\) | \(2.6094\) |
Rank
sage: E.rank()
The elliptic curves in class 86640cc have rank \(1\).
Complex multiplication
The elliptic curves in class 86640cc do not have complex multiplication.Modular form 86640.2.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.
