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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 33930g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33930.f4 | 33930g1 | \([1, -1, 0, -254835, -14126859]\) | \(2510581756496128561/1333551278592000\) | \(972158882093568000\) | \([2]\) | \(552960\) | \(2.1429\) | \(\Gamma_0(N)\)-optimal |
| 33930.f2 | 33930g2 | \([1, -1, 0, -2354355, 1380374325]\) | \(1979758117698975186481/17510434929000000\) | \(12765107063241000000\) | \([2, 2]\) | \(1105920\) | \(2.4895\) | |
| 33930.f3 | 33930g3 | \([1, -1, 0, -711675, 3269784861]\) | \(-54681655838565466801/6303365630859375000\) | \(-4595153544896484375000\) | \([2]\) | \(2211840\) | \(2.8361\) | |
| 33930.f1 | 33930g4 | \([1, -1, 0, -37589355, 88713845325]\) | \(8057323694463985606146481/638717154543000\) | \(465624805661847000\) | \([2]\) | \(2211840\) | \(2.8361\) |
Rank
sage: E.rank()
The elliptic curves in class 33930g have rank \(0\).
Complex multiplication
The elliptic curves in class 33930g do not have complex multiplication.Modular form 33930.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
