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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 7920.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7920.bc1 | 7920bf1 | \([0, 0, 0, -147, 1874]\) | \(-117649/440\) | \(-1313832960\) | \([]\) | \(2880\) | \(0.43535\) | \(\Gamma_0(N)\)-optimal |
| 7920.bc2 | 7920bf2 | \([0, 0, 0, 1293, -44494]\) | \(80062991/332750\) | \(-993586176000\) | \([]\) | \(8640\) | \(0.98465\) |
Rank
sage: E.rank()
The elliptic curves in class 7920.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 7920.bc do not have complex multiplication.Modular form 7920.2.a.bc
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.
