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SageMath
E = EllipticCurve("lv1")
E.isogeny_class()
Elliptic curves in class 141120lv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.dl3 | 141120lv1 | \([0, 0, 0, -71148, 6920368]\) | \(1771561/105\) | \(2360722772459520\) | \([2]\) | \(786432\) | \(1.7029\) | \(\Gamma_0(N)\)-optimal |
| 141120.dl2 | 141120lv2 | \([0, 0, 0, -212268, -29037008]\) | \(47045881/11025\) | \(247875891108249600\) | \([2, 2]\) | \(1572864\) | \(2.0494\) | |
| 141120.dl4 | 141120lv3 | \([0, 0, 0, 493332, -181164368]\) | \(590589719/972405\) | \(-21862653595747614720\) | \([2]\) | \(3145728\) | \(2.3960\) | |
| 141120.dl1 | 141120lv4 | \([0, 0, 0, -3175788, -2178181712]\) | \(157551496201/13125\) | \(295090346557440000\) | \([2]\) | \(3145728\) | \(2.3960\) |
Rank
sage: E.rank()
The elliptic curves in class 141120lv have rank \(1\).
Complex multiplication
The elliptic curves in class 141120lv do not have complex multiplication.Modular form 141120.2.a.lv
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.
