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Properties

Label 37830.k
Number of curves $2$
Conductor $37830$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 37830.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37830.k1 37830k2 \([1, 0, 1, -2338479, -1376608094]\) \(-1414242446350368771071209/2427151252032000\) \(-2427151252032000\) \([]\) \(798336\) \(2.2127\)  
37830.k2 37830k1 \([1, 0, 1, -20664, -2984498]\) \(-975745774860333049/3278815318120680\) \(-3278815318120680\) \([3]\) \(266112\) \(1.6634\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37830.k have rank \(0\).

Complex multiplication

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

Modular form 37830.2.a.k

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