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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 46800.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.bf1 | 46800cs2 | \([0, 0, 0, -157275, 24007050]\) | \(-8538302475/26\) | \(-1310100480000\) | \([]\) | \(186624\) | \(1.5523\) | |
| 46800.bf2 | 46800cs1 | \([0, 0, 0, -1275, 55850]\) | \(-3316275/17576\) | \(-1214853120000\) | \([]\) | \(62208\) | \(1.0030\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.bf have rank \(2\).
Complex multiplication
The elliptic curves in class 46800.bf do not have complex multiplication.Modular form 46800.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
