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Properties

Label 37030.h
Number of curves $2$
Conductor $37030$
CM no
Rank $1$
Graph

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

Elliptic curves in class 37030.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37030.h1 37030h2 \([1, -1, 0, -10479589, 11459511573]\) \(70665260180607/9411920000\) \(16952304757476838960000\) \([2]\) \(2967552\) \(2.9931\)  
37030.h2 37030h1 \([1, -1, 0, -2692709, -1518102635]\) \(1198785674367/140492800\) \(253048980636388966400\) \([2]\) \(1483776\) \(2.6465\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37030.h have rank \(1\).

Complex multiplication

The elliptic curves in class 37030.h do not have complex multiplication.

Modular form 37030.2.a.h

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.