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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 640.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 640.a1 | 640f1 | \([0, 1, 0, -66, -230]\) | \(252179168/25\) | \(3200\) | \([2]\) | \(64\) | \(-0.29271\) | \(\Gamma_0(N)\)-optimal |
| 640.a2 | 640f2 | \([0, 1, 0, -61, -261]\) | \(-1557376/625\) | \(-10240000\) | \([2]\) | \(128\) | \(0.053864\) |
Rank
sage: E.rank()
The elliptic curves in class 640.a have rank \(0\).
Complex multiplication
The elliptic curves in class 640.a do not have complex multiplication.Modular form 640.2.a.a
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.
