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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1155c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1155.j3 | 1155c1 | \([1, 1, 0, -203, 1032]\) | \(932288503609/779625\) | \(779625\) | \([2]\) | \(288\) | \(0.058449\) | \(\Gamma_0(N)\)-optimal |
| 1155.j2 | 1155c2 | \([1, 1, 0, -248, 483]\) | \(1697509118089/833765625\) | \(833765625\) | \([2, 2]\) | \(576\) | \(0.40502\) | |
| 1155.j1 | 1155c3 | \([1, 1, 0, -2123, -38142]\) | \(1058993490188089/13182390375\) | \(13182390375\) | \([2]\) | \(1152\) | \(0.75160\) | |
| 1155.j4 | 1155c4 | \([1, 1, 0, 907, 4872]\) | \(82375335041831/56396484375\) | \(-56396484375\) | \([2]\) | \(1152\) | \(0.75160\) |
Rank
sage: E.rank()
The elliptic curves in class 1155c have rank \(0\).
Complex multiplication
The elliptic curves in class 1155c do not have complex multiplication.Modular form 1155.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
