↑

Properties

Label 296450.jy
Number of curves $2$
Conductor $296450$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("jy1")
 
E.isogeny_class()
 

Elliptic curves in class 296450.jy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
296450.jy1 296450jy2 \([1, 1, 1, -3602838, -2633595469]\) \(544737993463/20000\) \(189889194687500000\) \([2]\) \(9830400\) \(2.4030\)  
296450.jy2 296450jy1 \([1, 1, 1, -214838, -45163469]\) \(-115501303/25600\) \(-243058169200000000\) \([2]\) \(4915200\) \(2.0565\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 296450.jy have rank \(0\).

Complex multiplication

The elliptic curves in class 296450.jy do not have complex multiplication.

Modular form 296450.2.a.jy

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{8} + q^{9} + 2 q^{12} - 2 q^{13} + q^{16} - 8 q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.