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SageMath
E = EllipticCurve("jb1")
E.isogeny_class()
Elliptic curves in class 397488jb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397488.jb3 | 397488jb1 | \([0, 1, 0, -59890952, -178192225548]\) | \(4649101309/6804\) | \(34769837722741390983168\) | \([2]\) | \(35942400\) | \(3.2269\) | \(\Gamma_0(N)\)-optimal |
| 397488.jb4 | 397488jb2 | \([0, 1, 0, -42666472, -282786157900]\) | \(-1680914269/5786802\) | \(-29571746983191553031184384\) | \([2]\) | \(71884800\) | \(3.5735\) | |
| 397488.jb1 | 397488jb3 | \([0, 1, 0, -1790951192, 29161439267988]\) | \(124318741396429/51631104\) | \(263845547843325091557408768\) | \([2]\) | \(179712000\) | \(4.0316\) | |
| 397488.jb2 | 397488jb4 | \([0, 1, 0, -1515359512, 38442374920340]\) | \(-75306487574989/81352871712\) | \(-415729886494009201294253359104\) | \([2]\) | \(359424000\) | \(4.3782\) |
Rank
sage: E.rank()
The elliptic curves in class 397488jb have rank \(1\).
Complex multiplication
The elliptic curves in class 397488jb do not have complex multiplication.Modular form 397488.2.a.jb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
