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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 22320bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22320.bi4 | 22320bv1 | \([0, 0, 0, 200013, -38629006]\) | \(296354077829711/387386634240\) | \(-1156730291654492160\) | \([2]\) | \(276480\) | \(2.1519\) | \(\Gamma_0(N)\)-optimal |
| 22320.bi3 | 22320bv2 | \([0, 0, 0, -1228467, -376607374]\) | \(68663623745397169/19216056254400\) | \(57378836518738329600\) | \([2]\) | \(552960\) | \(2.4985\) | |
| 22320.bi2 | 22320bv3 | \([0, 0, 0, -5709747, -5282825614]\) | \(-6894246873502147249/47925198774000\) | \(-143103876735983616000\) | \([2]\) | \(829440\) | \(2.7012\) | |
| 22320.bi1 | 22320bv4 | \([0, 0, 0, -91507827, -336926724046]\) | \(28379906689597370652529/1357352437500\) | \(4053032660736000000\) | \([2]\) | \(1658880\) | \(3.0478\) |
Rank
sage: E.rank()
The elliptic curves in class 22320bv have rank \(0\).
Complex multiplication
The elliptic curves in class 22320bv do not have complex multiplication.Modular form 22320.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
