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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 101640bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101640.m3 | 101640bv1 | \([0, -1, 0, -38276, 2894916]\) | \(13674725584/945\) | \(428576037120\) | \([2]\) | \(245760\) | \(1.2857\) | \(\Gamma_0(N)\)-optimal |
| 101640.m2 | 101640bv2 | \([0, -1, 0, -40696, 2510620]\) | \(4108974916/893025\) | \(1620017420313600\) | \([2, 2]\) | \(491520\) | \(1.6323\) | |
| 101640.m4 | 101640bv3 | \([0, -1, 0, 89984, 15212716]\) | \(22208984782/40516875\) | \(-147001580732160000\) | \([2]\) | \(983040\) | \(1.9788\) | |
| 101640.m1 | 101640bv4 | \([0, -1, 0, -210096, -34825140]\) | \(282678688658/18600435\) | \(67485297109063680\) | \([2]\) | \(983040\) | \(1.9788\) |
Rank
sage: E.rank()
The elliptic curves in class 101640bv have rank \(0\).
Complex multiplication
The elliptic curves in class 101640bv do not have complex multiplication.Modular form 101640.2.a.bv
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.
