Properties

Label 640.h
Number of curves $2$
Conductor $640$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 640.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
640.h1 640d2 \([0, -1, 0, -265, -1575]\) \(252179168/25\) \(204800\) \([2]\) \(128\) \(0.053864\)  
640.h2 640d1 \([0, -1, 0, -15, -25]\) \(-1557376/625\) \(-160000\) \([2]\) \(64\) \(-0.29271\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 640.h have rank \(0\).

Complex multiplication

The elliptic curves in class 640.h do not have complex multiplication.

Modular form 640.2.a.h

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{5} + q^{9} + 2 q^{11} - 2 q^{13} + 2 q^{15} + 6 q^{17} + 6 q^{19} + O(q^{20})\) 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.