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Properties

Label 37905.r
Number of curves $2$
Conductor $37905$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 37905.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37905.r1 37905q2 \([1, 0, 1, -1803203, -932037577]\) \(2009438972659/275625\) \(88940796700336875\) \([2]\) \(729600\) \(2.2701\)  
37905.r2 37905q1 \([1, 0, 1, -122748, -11820419]\) \(633839779/180075\) \(58107987177553425\) \([2]\) \(364800\) \(1.9235\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37905.r have rank \(1\).

Complex multiplication

The elliptic curves in class 37905.r do not have complex multiplication.

Modular form 37905.2.a.r

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