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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1980.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1980.b1 | 1980a2 | \([0, 0, 0, -543, -4858]\) | \(94875856/275\) | \(51321600\) | \([2]\) | \(576\) | \(0.35023\) | |
| 1980.b2 | 1980a1 | \([0, 0, 0, -48, -7]\) | \(1048576/605\) | \(7056720\) | \([2]\) | \(288\) | \(0.0036590\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1980.b have rank \(1\).
Complex multiplication
The elliptic curves in class 1980.b do not have complex multiplication.Modular form 1980.2.a.b
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.
