↑

Properties

Label 259182h
Number of curves $2$
Conductor $259182$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 259182h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.h2 259182h1 \([1, -1, 0, 52794, -36877032]\) \(12600539783/461862324\) \(-596480397533899956\) \([]\) \(4423680\) \(2.0907\) \(\Gamma_0(N)\)-optimal
259182.h1 259182h2 \([1, -1, 0, -6954921, -7060224627]\) \(-28808239025774377/10677167424\) \(-13789219727746241856\) \([]\) \(13271040\) \(2.6400\)  

Rank

sage: E.rank()
 

The elliptic curves in class 259182h have rank \(1\).

Complex multiplication

The elliptic curves in class 259182h do not have complex multiplication.

Modular form 259182.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{5} - q^{7} - q^{8} + 3 q^{10} - 5 q^{13} + q^{14} + q^{16} - q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.