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Properties

Label 650.h
Number of curves $2$
Conductor $650$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 650.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
650.h1 650l2 \([1, 0, 0, -283263, -58050983]\) \(-6434774386429585/140608\) \(-54925000000\) \([]\) \(5400\) \(1.5871\)  
650.h2 650l1 \([1, 0, 0, -3263, -90983]\) \(-9836106385/3407872\) \(-1331200000000\) \([3]\) \(1800\) \(1.0378\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 650.h have rank \(0\).

Complex multiplication

The elliptic curves in class 650.h do not have complex multiplication.

Modular form 650.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} - 2 q^{6} + 5 q^{7} + q^{8} + q^{9} - 3 q^{11} - 2 q^{12} + q^{13} + 5 q^{14} + q^{16} + 3 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.