Properties

Label 4290b
Number of curves $4$
Conductor $4290$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 4290b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4290.b4 4290b1 \([1, 1, 0, -1749568, 325439488]\) \(592265697637387401314569/296787655248366796800\) \(296787655248366796800\) \([2]\) \(168960\) \(2.6211\) \(\Gamma_0(N)\)-optimal
4290.b2 4290b2 \([1, 1, 0, -22721088, 41643528192]\) \(1297212465095901089487274249/1193746061037404160000\) \(1193746061037404160000\) \([2, 2]\) \(337920\) \(2.9676\)  
4290.b1 4290b3 \([1, 1, 0, -363457088, 2666878113792]\) \(5309860874757074224246393258249/4502770931800627200\) \(4502770931800627200\) \([2]\) \(675840\) \(3.3142\)  
4290.b3 4290b4 \([1, 1, 0, -17529408, 61186050048]\) \(-595697118196750093952139529/1272946549598037600000000\) \(-1272946549598037600000000\) \([2]\) \(675840\) \(3.3142\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4290b have rank \(0\).

Complex multiplication

The elliptic curves in class 4290b do not have complex multiplication.

Modular form 4290.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} + q^{11} - q^{12} - q^{13} + q^{15} + q^{16} + 6 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display

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.