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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 83490d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83490.c4 | 83490d1 | \([1, 1, 0, -543413, 273714093]\) | \(-10017490085065009/12502381363200\) | \(-22148731230171955200\) | \([2]\) | \(2580480\) | \(2.4054\) | \(\Gamma_0(N)\)-optimal |
| 83490.c3 | 83490d2 | \([1, 1, 0, -10455733, 13003115437]\) | \(71356102305927901489/35540674560000\) | \(62962472964188160000\) | \([2, 2]\) | \(5160960\) | \(2.7520\) | |
| 83490.c2 | 83490d3 | \([1, 1, 0, -12236853, 8268542253]\) | \(114387056741228939569/49503729150000000\) | \(87698875916703150000000\) | \([2]\) | \(10321920\) | \(3.0986\) | |
| 83490.c1 | 83490d4 | \([1, 1, 0, -167271733, 832617621037]\) | \(292169767125103365085489/72534787200\) | \(128499800146819200\) | \([2]\) | \(10321920\) | \(3.0986\) |
Rank
sage: E.rank()
The elliptic curves in class 83490d have rank \(0\).
Complex multiplication
The elliptic curves in class 83490d do not have complex multiplication.Modular form 83490.2.a.d
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.
