Show commands:
SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 35280cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.bt4 | 35280cw1 | \([0, 0, 0, -6468, 164983]\) | \(588791808/109375\) | \(5558915250000\) | \([2]\) | \(55296\) | \(1.1637\) | \(\Gamma_0(N)\)-optimal |
| 35280.bt3 | 35280cw2 | \([0, 0, 0, -98343, 11869858]\) | \(129348709488/6125\) | \(4980788064000\) | \([2]\) | \(110592\) | \(1.5103\) | |
| 35280.bt2 | 35280cw3 | \([0, 0, 0, -153468, -23124717]\) | \(10788913152/8575\) | \(317712018632400\) | \([2]\) | \(165888\) | \(1.7130\) | |
| 35280.bt1 | 35280cw4 | \([0, 0, 0, -186543, -12428262]\) | \(1210991472/588245\) | \(348720711650922240\) | \([2]\) | \(331776\) | \(2.0596\) |
Rank
sage: E.rank()
The elliptic curves in class 35280cw have rank \(1\).
Complex multiplication
The elliptic curves in class 35280cw do not have complex multiplication.Modular form 35280.2.a.cw
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.
