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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 2790l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2790.k4 | 2790l1 | \([1, -1, 0, 12501, 600453]\) | \(296354077829711/387386634240\) | \(-282404856360960\) | \([2]\) | \(11520\) | \(1.4587\) | \(\Gamma_0(N)\)-optimal |
| 2790.k3 | 2790l2 | \([1, -1, 0, -76779, 5903685]\) | \(68663623745397169/19216056254400\) | \(14008505009457600\) | \([2]\) | \(23040\) | \(1.8053\) | |
| 2790.k2 | 2790l3 | \([1, -1, 0, -356859, 82633365]\) | \(-6894246873502147249/47925198774000\) | \(-34937469906246000\) | \([6]\) | \(34560\) | \(2.0081\) | |
| 2790.k1 | 2790l4 | \([1, -1, 0, -5719239, 5265909873]\) | \(28379906689597370652529/1357352437500\) | \(989509926937500\) | \([6]\) | \(69120\) | \(2.3546\) |
Rank
sage: E.rank()
The elliptic curves in class 2790l have rank \(0\).
Complex multiplication
The elliptic curves in class 2790l do not have complex multiplication.Modular form 2790.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
