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SageMath
E = EllipticCurve("gq1")
E.isogeny_class()
Elliptic curves in class 142800gq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142800.jb3 | 142800gq1 | \([0, 1, 0, -2983, -63712]\) | \(11745974272/357\) | \(89250000\) | \([2]\) | \(81920\) | \(0.62345\) | \(\Gamma_0(N)\)-optimal |
| 142800.jb2 | 142800gq2 | \([0, 1, 0, -3108, -58212]\) | \(830321872/127449\) | \(509796000000\) | \([2, 2]\) | \(163840\) | \(0.97002\) | |
| 142800.jb1 | 142800gq3 | \([0, 1, 0, -13608, 550788]\) | \(17418812548/1753941\) | \(28063056000000\) | \([2]\) | \(327680\) | \(1.3166\) | |
| 142800.jb4 | 142800gq4 | \([0, 1, 0, 5392, -313212]\) | \(1083360092/3306177\) | \(-52898832000000\) | \([2]\) | \(327680\) | \(1.3166\) |
Rank
sage: E.rank()
The elliptic curves in class 142800gq have rank \(1\).
Complex multiplication
The elliptic curves in class 142800gq do not have complex multiplication.Modular form 142800.2.a.gq
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.
