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Properties

Label 165649.h
Number of curves $2$
Conductor $165649$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 165649.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
165649.h1 165649h2 \([0, 1, 1, -682363447, 6860524945830]\) \(-5646782660608/11\) \(-68448287752545147491\) \([]\) \(27332640\) \(3.4869\)  
165649.h2 165649h1 \([0, 1, 1, -8172017, 9998406457]\) \(-9699328/1331\) \(-8282242818057962846411\) \([]\) \(9110880\) \(2.9376\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 165649.h have rank \(0\).

Complex multiplication

The elliptic curves in class 165649.h do not have complex multiplication.

Modular form 165649.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} - 3 q^{5} - 2 q^{7} - 2 q^{9} - 2 q^{12} + 4 q^{13} - 3 q^{15} + 4 q^{16} - 6 q^{17} - 2 q^{19} + O(q^{20})\) 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 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.