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Properties

Label 37830.n
Number of curves $4$
Conductor $37830$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 37830.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37830.n1 37830l4 \([1, 0, 1, -40678, 3153698]\) \(7443670502851916761/1847167968750\) \(1847167968750\) \([2]\) \(112128\) \(1.3413\)  
37830.n2 37830l3 \([1, 0, 1, -19098, -990494]\) \(770290762139049241/23305333223250\) \(23305333223250\) \([2]\) \(112128\) \(1.3413\)  
37830.n3 37830l2 \([1, 0, 1, -2848, 36506]\) \(2553432858309241/894443062500\) \(894443062500\) \([2, 2]\) \(56064\) \(0.99469\)  
37830.n4 37830l1 \([1, 0, 1, 532, 4058]\) \(16696735751879/16622502000\) \(-16622502000\) \([2]\) \(28032\) \(0.64811\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37830.n have rank \(1\).

Complex multiplication

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

Modular form 37830.2.a.n

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.