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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 11550.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11550.r1 | 11550i4 | \([1, 1, 0, -1006175, 388051875]\) | \(7209828390823479793/49509306\) | \(773582906250\) | \([2]\) | \(98304\) | \(1.8809\) | |
| 11550.r2 | 11550i3 | \([1, 1, 0, -87675, 813375]\) | \(4770223741048753/2740574865798\) | \(42821482278093750\) | \([2]\) | \(98304\) | \(1.8809\) | |
| 11550.r3 | 11550i2 | \([1, 1, 0, -62925, 6035625]\) | \(1763535241378513/4612311396\) | \(72067365562500\) | \([2, 2]\) | \(49152\) | \(1.5344\) | |
| 11550.r4 | 11550i1 | \([1, 1, 0, -2425, 167125]\) | \(-100999381393/723148272\) | \(-11299191750000\) | \([2]\) | \(24576\) | \(1.1878\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11550.r have rank \(1\).
Complex multiplication
The elliptic curves in class 11550.r do not have complex multiplication.Modular form 11550.2.a.r
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.
