Properties

Label 259210ce
Number of curves $2$
Conductor $259210$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 259210ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259210.ce2 259210ce1 \([1, 1, 1, -1840931, 1129849153]\) \(-115501303/25600\) \(-152928821417001548800\) \([2]\) \(13798400\) \(2.5935\) \(\Gamma_0(N)\)-optimal
259210.ce1 259210ce2 \([1, 1, 1, -30872451, 66009490049]\) \(544737993463/20000\) \(119475641732032460000\) \([2]\) \(27596800\) \(2.9401\)  

Rank

sage: E.rank()
 

The elliptic curves in class 259210ce have rank \(0\).

Complex multiplication

The elliptic curves in class 259210ce do not have complex multiplication.

Modular form 259210.2.a.ce

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} - q^{5} + 2 q^{6} + q^{8} + q^{9} - q^{10} + 4 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} + q^{16} - 8 q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.