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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 7590q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7590.q4 | 7590q1 | \([1, 1, 1, 9, -1587]\) | \(80062991/1092960000\) | \(-1092960000\) | \([2]\) | \(3840\) | \(0.41325\) | \(\Gamma_0(N)\)-optimal |
| 7590.q3 | 7590q2 | \([1, 1, 1, -1991, -34387]\) | \(872873131105009/18665024400\) | \(18665024400\) | \([2, 2]\) | \(7680\) | \(0.75982\) | |
| 7590.q1 | 7590q3 | \([1, 1, 1, -31691, -2184667]\) | \(3519916805915669809/1662255540\) | \(1662255540\) | \([2]\) | \(15360\) | \(1.1064\) | |
| 7590.q2 | 7590q4 | \([1, 1, 1, -4291, 56693]\) | \(8737870045868209/3579180733260\) | \(3579180733260\) | \([2]\) | \(15360\) | \(1.1064\) |
Rank
sage: E.rank()
The elliptic curves in class 7590q have rank \(0\).
Complex multiplication
The elliptic curves in class 7590q do not have complex multiplication.Modular form 7590.2.a.q
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.
