Properties

Label 450840.h
Number of curves $2$
Conductor $450840$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 450840.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450840.h1 450840h1 \([0, -1, 0, -4771, 128440]\) \(152818608128/7605\) \(597813840\) \([2]\) \(409600\) \(0.75529\) \(\Gamma_0(N)\)-optimal
450840.h2 450840h2 \([0, -1, 0, -4516, 142516]\) \(-8100185168/2142075\) \(-2694147705600\) \([2]\) \(819200\) \(1.1019\)  

Rank

sage: E.rank()
 

The elliptic curves in class 450840.h have rank \(2\).

Complex multiplication

The elliptic curves in class 450840.h do not have complex multiplication.

Modular form 450840.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 4q^{11} + q^{13} + q^{15} + 4q^{19} + O(q^{20})\)  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.