Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 155610x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 155610.ek4 | 155610x1 | \([1, -1, 1, 7843, -470811]\) | \(73197245859191/172623360000\) | \(-125842429440000\) | \([4]\) | \(491520\) | \(1.3895\) | \(\Gamma_0(N)\)-optimal |
| 155610.ek3 | 155610x2 | \([1, -1, 1, -64157, -5165211]\) | \(40061018056412809/7275103617600\) | \(5303550537230400\) | \([2, 2]\) | \(983040\) | \(1.7361\) | |
| 155610.ek2 | 155610x3 | \([1, -1, 1, -303557, 59664309]\) | \(4243415895694547209/351514682293320\) | \(256254203391830280\) | \([2]\) | \(1966080\) | \(2.0826\) | |
| 155610.ek1 | 155610x4 | \([1, -1, 1, -976757, -371300331]\) | \(141369383441705190409/6345626621880\) | \(4625961807350520\) | \([2]\) | \(1966080\) | \(2.0826\) |
Rank
sage: E.rank()
The elliptic curves in class 155610x have rank \(1\).
Complex multiplication
The elliptic curves in class 155610x do not have complex multiplication.Modular form 155610.2.a.x
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.
