Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 152880x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.hf3 | 152880x1 | \([0, 1, 0, -4720, 799700]\) | \(-24137569/561600\) | \(-270629594726400\) | \([2]\) | \(414720\) | \(1.4500\) | \(\Gamma_0(N)\)-optimal |
| 152880.hf2 | 152880x2 | \([0, 1, 0, -161520, 24821460]\) | \(967068262369/4928040\) | \(2374774693724160\) | \([2]\) | \(829440\) | \(1.7966\) | |
| 152880.hf4 | 152880x3 | \([0, 1, 0, 42320, -21158572]\) | \(17394111071/411937500\) | \(-198508687104000000\) | \([2]\) | \(1244160\) | \(1.9994\) | |
| 152880.hf1 | 152880x4 | \([0, 1, 0, -937680, -332014572]\) | \(189208196468929/10860320250\) | \(5233483026809856000\) | \([2]\) | \(2488320\) | \(2.3459\) |
Rank
sage: E.rank()
The elliptic curves in class 152880x have rank \(1\).
Complex multiplication
The elliptic curves in class 152880x do not have complex multiplication.Modular form 152880.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
