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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 45504.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 45504.bv1 | 45504bn3 | \([0, 0, 0, -3004716, -2004715568]\) | \(15698803397448457/20709376\) | \(3957623384702976\) | \([]\) | \(691200\) | \(2.2689\) | |
| 45504.bv2 | 45504bn2 | \([0, 0, 0, -46956, -1174448]\) | \(59914169497/31554496\) | \(6030158091780096\) | \([]\) | \(230400\) | \(1.7196\) | |
| 45504.bv3 | 45504bn1 | \([0, 0, 0, -26796, 1688272]\) | \(11134383337/316\) | \(60388540416\) | \([]\) | \(76800\) | \(1.1703\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 45504.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 45504.bv do not have complex multiplication.Modular form 45504.2.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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
