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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 38808.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38808.cc1 | 38808ce4 | \([0, 0, 0, -282342459, -1294787288522]\) | \(14171198121996897746/4077720290568771\) | \(716247555778716410690131968\) | \([2]\) | \(17694720\) | \(3.8594\) | |
| 38808.cc2 | 38808ce2 | \([0, 0, 0, -258863619, -1602881322770]\) | \(21843440425782779332/3100814593569\) | \(272327515781739188069376\) | \([2, 2]\) | \(8847360\) | \(3.5128\) | |
| 38808.cc3 | 38808ce1 | \([0, 0, 0, -258854799, -1602996023342]\) | \(87364831012240243408/1760913\) | \(38662829421689088\) | \([2]\) | \(4423680\) | \(3.1663\) | \(\Gamma_0(N)\)-optimal |
| 38808.cc4 | 38808ce3 | \([0, 0, 0, -235525899, -1903634520410]\) | \(-8226100326647904626/4152140742401883\) | \(-729319434899189202955966464\) | \([2]\) | \(17694720\) | \(3.8594\) |
Rank
sage: E.rank()
The elliptic curves in class 38808.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 38808.cc do not have complex multiplication.Modular form 38808.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
