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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 83490.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83490.l1 | 83490n6 | \([1, 1, 0, -359209072, 2620259170984]\) | \(2893406764219154648621281/23959804908600\) | \(42446255943684324600\) | \([2]\) | \(14745600\) | \(3.3540\) | |
| 83490.l2 | 83490n4 | \([1, 1, 0, -22466072, 40875139584]\) | \(707862768889380029281/2032621157160000\) | \(3600912369799526760000\) | \([2, 2]\) | \(7372800\) | \(3.0075\) | |
| 83490.l3 | 83490n3 | \([1, 1, 0, -21149592, -37309693824]\) | \(590573036229385476961/2480892013702080\) | \(4395051536686070546880\) | \([2]\) | \(7372800\) | \(3.0075\) | |
| 83490.l4 | 83490n5 | \([1, 1, 0, -13449152, 74008713816]\) | \(-151863133743301125601/1247970610321875000\) | \(-2210856062392431196875000\) | \([2]\) | \(14745600\) | \(3.3540\) | |
| 83490.l5 | 83490n2 | \([1, 1, 0, -1983192, 60952896]\) | \(486925174907883361/280854696038400\) | \(497551226168483942400\) | \([2, 2]\) | \(3686400\) | \(2.6609\) | |
| 83490.l6 | 83490n1 | \([1, 1, 0, 494888, 7921984]\) | \(7566359979929759/4393197895680\) | \(-7782818057268756480\) | \([2]\) | \(1843200\) | \(2.3143\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 83490.l have rank \(0\).
Complex multiplication
The elliptic curves in class 83490.l do not have complex multiplication.Modular form 83490.2.a.l
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
