Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 160446i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160446.bo3 | 160446i1 | \([1, 0, 0, -12139388, -10542660336]\) | \(111675519439697265625/37528570137307392\) | \(66484151241018420678912\) | \([2]\) | \(18247680\) | \(3.0817\) | \(\Gamma_0(N)\)-optimal |
| 160446.bo4 | 160446i2 | \([1, 0, 0, 35418452, -72852942304]\) | \(2773679829880629422375/2899504554614368272\) | \(-5136649188277184870312592\) | \([2]\) | \(36495360\) | \(3.4283\) | |
| 160446.bo1 | 160446i3 | \([1, 0, 0, -398721683, 3063902480673]\) | \(3957101249824708884951625/772310238681366528\) | \(1368194698748600367710208\) | \([2]\) | \(54743040\) | \(3.6310\) | |
| 160446.bo2 | 160446i4 | \([1, 0, 0, -356594323, 3736617441569]\) | \(-2830680648734534916567625/1766676274677722124288\) | \(-3129774787844340084225773568\) | \([2]\) | \(109486080\) | \(3.9776\) |
Rank
sage: E.rank()
The elliptic curves in class 160446i have rank \(0\).
Complex multiplication
The elliptic curves in class 160446i do not have complex multiplication.Modular form 160446.2.a.i
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.
