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SageMath
E = EllipticCurve("le1")
E.isogeny_class()
Elliptic curves in class 242550.le
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.le1 | 242550le6 | \([1, -1, 1, -1886212355, -31530255337353]\) | \(553808571467029327441/12529687500\) | \(16790979597143554687500\) | \([2]\) | \(113246208\) | \(3.7887\) | |
| 242550.le2 | 242550le3 | \([1, -1, 1, -130370855, 571730641647]\) | \(182864522286982801/463015182960\) | \(620484628227882783750000\) | \([2]\) | \(56623104\) | \(3.4422\) | |
| 242550.le3 | 242550le4 | \([1, -1, 1, -118022855, -491456854353]\) | \(135670761487282321/643043610000\) | \(861739938492762656250000\) | \([2, 2]\) | \(56623104\) | \(3.4422\) | |
| 242550.le4 | 242550le5 | \([1, -1, 1, -57385355, -995839579353]\) | \(-15595206456730321/310672490129100\) | \(-416330849684120253454687500\) | \([2]\) | \(113246208\) | \(3.7887\) | |
| 242550.le5 | 242550le2 | \([1, -1, 1, -11300855, 1385341647]\) | \(119102750067601/68309049600\) | \(91540659584196900000000\) | \([2, 2]\) | \(28311552\) | \(3.0956\) | |
| 242550.le6 | 242550le1 | \([1, -1, 1, 2811145, 171709647]\) | \(1833318007919/1070530560\) | \(-1434613336611840000000\) | \([2]\) | \(14155776\) | \(2.7490\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 242550.le have rank \(0\).
Complex multiplication
The elliptic curves in class 242550.le do not have complex multiplication.Modular form 242550.2.a.le
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
