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Properties

Label 37830h
Number of curves $2$
Conductor $37830$
CM no
Rank $2$
Graph

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

Elliptic curves in class 37830h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37830.g1 37830h1 \([1, 1, 0, -1415277, 646611741]\) \(313507935617703592835161/476491440114892800\) \(476491440114892800\) \([2]\) \(798720\) \(2.2920\) \(\Gamma_0(N)\)-optimal
37830.g2 37830h2 \([1, 1, 0, -1000557, 1033711389]\) \(-110777075176926344149081/397882904745605760000\) \(-397882904745605760000\) \([2]\) \(1597440\) \(2.6386\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37830h have rank \(2\).

Complex multiplication

The elliptic curves in class 37830h do not have complex multiplication.

Modular form 37830.2.a.h

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