Show commands:
SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 202800br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202800.gb4 | 202800br1 | \([0, 1, 0, -19504008, -54778464012]\) | \(-2656166199049/2658140160\) | \(-821141430243164160000000\) | \([2]\) | \(30965760\) | \(3.2845\) | \(\Gamma_0(N)\)-optimal |
| 202800.gb3 | 202800br2 | \([0, 1, 0, -365616008, -2690075232012]\) | \(17496824387403529/6580454400\) | \(2032806177408614400000000\) | \([2, 2]\) | \(61931520\) | \(3.6310\) | |
| 202800.gb2 | 202800br3 | \([0, 1, 0, -419696008, -1841992672012]\) | \(26465989780414729/10571870144160\) | \(3265817469354418268160000000\) | \([2]\) | \(123863040\) | \(3.9776\) | |
| 202800.gb1 | 202800br4 | \([0, 1, 0, -5849328008, -172191613152012]\) | \(71647584155243142409/10140000\) | \(3132405968640000000000\) | \([2]\) | \(123863040\) | \(3.9776\) |
Rank
sage: E.rank()
The elliptic curves in class 202800br have rank \(1\).
Complex multiplication
The elliptic curves in class 202800br do not have complex multiplication.Modular form 202800.2.a.br
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.
