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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 17640.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17640.n1 | 17640c1 | \([0, 0, 0, -140238, 19753713]\) | \(8232302592/214375\) | \(7942800465810000\) | \([2]\) | \(110592\) | \(1.8326\) | \(\Gamma_0(N)\)-optimal |
| 17640.n2 | 17640c2 | \([0, 0, 0, 25137, 63511938]\) | \(2963088/2941225\) | \(-1743603558254611200\) | \([2]\) | \(221184\) | \(2.1792\) |
Rank
sage: E.rank()
The elliptic curves in class 17640.n have rank \(0\).
Complex multiplication
The elliptic curves in class 17640.n do not have complex multiplication.Modular form 17640.2.a.n
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.
