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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 7650.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7650.bo1 | 7650bv2 | \([1, -1, 1, -1494230, 726071397]\) | \(-32391289681150609/1228250000000\) | \(-13990535156250000000\) | \([]\) | \(181440\) | \(2.4438\) | |
| 7650.bo2 | 7650bv1 | \([1, -1, 1, 89770, 3191397]\) | \(7023836099951/4456448000\) | \(-50761728000000000\) | \([]\) | \(60480\) | \(1.8945\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7650.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 7650.bo do not have complex multiplication.Modular form 7650.2.a.bo
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
