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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 369600.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.ci1 | 369600ci4 | \([0, -1, 0, -425780033, -3381487788063]\) | \(2084105208962185000201/31185000\) | \(127733760000000000\) | \([2]\) | \(56623104\) | \(3.2860\) | |
| 369600.ci2 | 369600ci3 | \([0, -1, 0, -28852033, -43406636063]\) | \(648474704552553481/176469171805080\) | \(722817727713607680000000\) | \([2]\) | \(56623104\) | \(3.2860\) | |
| 369600.ci3 | 369600ci2 | \([0, -1, 0, -26612033, -52825836063]\) | \(508859562767519881/62240270400\) | \(254936147558400000000\) | \([2, 2]\) | \(28311552\) | \(2.9394\) | |
| 369600.ci4 | 369600ci1 | \([0, -1, 0, -1524033, -968940063]\) | \(-95575628340361/43812679680\) | \(-179456735969280000000\) | \([2]\) | \(14155776\) | \(2.5928\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.ci do not have complex multiplication.Modular form 369600.2.a.ci
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
