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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 93600.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 93600.bf1 | 93600z2 | \([0, 0, 0, -297075, -62302250]\) | \(497169541448/190125\) | \(1108809000000000\) | \([2]\) | \(737280\) | \(1.8528\) | |
| 93600.bf2 | 93600z1 | \([0, 0, 0, -15825, -1271000]\) | \(-601211584/609375\) | \(-444234375000000\) | \([2]\) | \(368640\) | \(1.5062\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 93600.bf have rank \(2\).
Complex multiplication
The elliptic curves in class 93600.bf do not have complex multiplication.Modular form 93600.2.a.bf
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.
