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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 32490l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32490.c4 | 32490l1 | \([1, -1, 0, 40545, -2749235]\) | \(214921799/218880\) | \(-7506806373861120\) | \([2]\) | \(368640\) | \(1.7331\) | \(\Gamma_0(N)\)-optimal |
| 32490.c3 | 32490l2 | \([1, -1, 0, -219375, -25154339]\) | \(34043726521/11696400\) | \(401144965603203600\) | \([2, 2]\) | \(737280\) | \(2.0796\) | |
| 32490.c2 | 32490l3 | \([1, -1, 0, -1453995, 656602825]\) | \(9912050027641/311647500\) | \(10688402044032727500\) | \([2]\) | \(1474560\) | \(2.4262\) | |
| 32490.c1 | 32490l4 | \([1, -1, 0, -3143475, -2143957199]\) | \(100162392144121/23457780\) | \(804518514348647220\) | \([2]\) | \(1474560\) | \(2.4262\) |
Rank
sage: E.rank()
The elliptic curves in class 32490l have rank \(1\).
Complex multiplication
The elliptic curves in class 32490l do not have complex multiplication.Modular form 32490.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
