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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 17680.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17680.e1 | 17680g1 | \([0, 0, 0, -283, -822]\) | \(611960049/282880\) | \(1158676480\) | \([2]\) | \(6144\) | \(0.43387\) | \(\Gamma_0(N)\)-optimal |
| 17680.e2 | 17680g2 | \([0, 0, 0, 997, -6198]\) | \(26757728271/19536400\) | \(-80021094400\) | \([2]\) | \(12288\) | \(0.78045\) |
Rank
sage: E.rank()
The elliptic curves in class 17680.e have rank \(1\).
Complex multiplication
The elliptic curves in class 17680.e do not have complex multiplication.Modular form 17680.2.a.e
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.
