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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 96600.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96600.bp1 | 96600bj2 | \([0, 1, 0, -63208, -3544912]\) | \(6982110826/2699487\) | \(10797948000000000\) | \([2]\) | \(768000\) | \(1.7755\) | |
| 96600.bp2 | 96600bj1 | \([0, 1, 0, -28208, 1775088]\) | \(1241154932/30429\) | \(60858000000000\) | \([2]\) | \(384000\) | \(1.4289\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96600.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 96600.bp do not have complex multiplication.Modular form 96600.2.a.bp
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
