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Properties

Label 187850.h
Number of curves $2$
Conductor $187850$
CM no
Rank $1$
Graph

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

Elliptic curves in class 187850.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187850.h1 187850ba2 \([1, 0, 1, -3274521, -2280980932]\) \(-6434774386429585/140608\) \(-84848382548800\) \([]\) \(5443200\) \(2.1990\)  
187850.h2 187850ba1 \([1, 0, 1, -37721, -3568452]\) \(-9836106385/3407872\) \(-2056443638579200\) \([]\) \(1814400\) \(1.6497\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 187850.h have rank \(1\).

Complex multiplication

The elliptic curves in class 187850.h do not have complex multiplication.

Modular form 187850.2.a.h

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