Properties

Label 930.h
Number of curves $2$
Conductor $930$
CM no
Rank $1$
Graph

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

Elliptic curves in class 930.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.h1 930h2 \([1, 0, 1, -2013, -12344]\) \(901456690969801/457629750000\) \(457629750000\) \([2]\) \(1920\) \(0.92991\)  
930.h2 930h1 \([1, 0, 1, 467, -1432]\) \(11298232190519/7472736000\) \(-7472736000\) \([2]\) \(960\) \(0.58334\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 930.h have rank \(1\).

Complex multiplication

The elliptic curves in class 930.h do not have complex multiplication.

Modular form 930.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 2q^{7} - q^{8} + q^{9} - q^{10} - 4q^{11} + q^{12} - 4q^{13} + 2q^{14} + q^{15} + q^{16} + 2q^{17} - q^{18} - 8q^{19} + O(q^{20})\)  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.