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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 65088.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65088.bv1 | 65088ba2 | \([0, 0, 0, -4101708, 35483575664]\) | \(-39934705050538129/2823126576537804\) | \(-539507890401066120904704\) | \([]\) | \(5419008\) | \(3.2335\) | |
| 65088.bv2 | 65088ba1 | \([0, 0, 0, -956748, -362678416]\) | \(-506814405937489/4048994304\) | \(-773774861301448704\) | \([]\) | \(774144\) | \(2.2605\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 65088.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 65088.bv do not have complex multiplication.Modular form 65088.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
