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SageMath
E = EllipticCurve("jb1")
E.isogeny_class()
Elliptic curves in class 116160.jb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116160.jb1 | 116160jd4 | \([0, 1, 0, -120998225, -512331200625]\) | \(6749703004355978704/5671875\) | \(164627620608000000\) | \([2]\) | \(6635520\) | \(3.0391\) | |
| 116160.jb2 | 116160jd3 | \([0, 1, 0, -7560725, -8010763125]\) | \(-26348629355659264/24169921875\) | \(-43846134750000000000\) | \([2]\) | \(3317760\) | \(2.6925\) | |
| 116160.jb3 | 116160jd2 | \([0, 1, 0, -1527665, -669713937]\) | \(13584145739344/1195803675\) | \(34708507103832883200\) | \([2]\) | \(2211840\) | \(2.4898\) | |
| 116160.jb4 | 116160jd1 | \([0, 1, 0, 105835, -48657237]\) | \(72268906496/606436875\) | \(-1100124074712960000\) | \([2]\) | \(1105920\) | \(2.1432\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116160.jb have rank \(1\).
Complex multiplication
The elliptic curves in class 116160.jb do not have complex multiplication.Modular form 116160.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
