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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 14490.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.cc1 | 14490cc1 | \([1, -1, 1, -33974222, 76192396701]\) | \(5949010462538271898545049/3314625947988102720\) | \(2416362316083326882880\) | \([2]\) | \(1697280\) | \(3.0505\) | \(\Gamma_0(N)\)-optimal |
| 14490.cc2 | 14490cc2 | \([1, -1, 1, -27923702, 104184522429]\) | \(-3303050039017428591035929/4519896503737558217400\) | \(-3295004551224679940484600\) | \([2]\) | \(3394560\) | \(3.3971\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 14490.cc do not have complex multiplication.Modular form 14490.2.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 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.
