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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 1155.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1155.k1 | 1155f3 | \([1, 1, 0, -20702, -333459]\) | \(981281029968144361/522287841796875\) | \(522287841796875\) | \([4]\) | \(4608\) | \(1.5155\) | |
| 1155.k2 | 1155f2 | \([1, 1, 0, -16247, -803016]\) | \(474334834335054841/607815140625\) | \(607815140625\) | \([2, 2]\) | \(2304\) | \(1.1689\) | |
| 1155.k3 | 1155f1 | \([1, 1, 0, -16242, -803529]\) | \(473897054735271721/779625\) | \(779625\) | \([2]\) | \(1152\) | \(0.82233\) | \(\Gamma_0(N)\)-optimal |
| 1155.k4 | 1155f4 | \([1, 1, 0, -11872, -1239641]\) | \(-185077034913624841/551466161890875\) | \(-551466161890875\) | \([2]\) | \(4608\) | \(1.5155\) |
Rank
sage: E.rank()
The elliptic curves in class 1155.k have rank \(1\).
Complex multiplication
The elliptic curves in class 1155.k do not have complex multiplication.Modular form 1155.2.a.k
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.
