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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 20181g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20181.i3 | 20181g1 | \([0, -1, 1, 21783, 2684135]\) | \(1287913472/4271211\) | \(-3790715484827691\) | \([]\) | \(92160\) | \(1.6724\) | \(\Gamma_0(N)\)-optimal |
| 20181.i2 | 20181g2 | \([0, -1, 1, -1016097, 395288192]\) | \(-130725250859008/275894451\) | \(-244857340829974131\) | \([]\) | \(276480\) | \(2.2217\) | |
| 20181.i1 | 20181g3 | \([0, -1, 1, -82345527, 287640199565]\) | \(-69578264895333695488/651\) | \(-577764896331\) | \([]\) | \(829440\) | \(2.7710\) |
Rank
sage: E.rank()
The elliptic curves in class 20181g have rank \(1\).
Complex multiplication
The elliptic curves in class 20181g do not have complex multiplication.Modular form 20181.2.a.g
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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
