↑

Properties

Label 292494.p
Number of curves $2$
Conductor $292494$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 292494.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
292494.p1 292494p2 \([1, 1, 1, -10945026, -13982457075]\) \(-30526075007211889/103499257854\) \(-491632263672637958814\) \([]\) \(13445600\) \(2.8344\)  
292494.p2 292494p1 \([1, 1, 1, -1716, 9447285]\) \(-117649/8118144\) \(-38562030243448704\) \([]\) \(1920800\) \(1.8615\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 292494.p have rank \(0\).

Complex multiplication

The elliptic curves in class 292494.p do not have complex multiplication.

Modular form 292494.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - q^{7} + q^{8} + q^{9} - q^{10} + 2 q^{11} - q^{12} - q^{14} + q^{15} + q^{16} + 3 q^{17} + q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.