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Properties

Label 37570.b
Number of curves $2$
Conductor $37570$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 37570.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37570.b1 37570c2 \([1, 0, 1, -10261674, -12653325028]\) \(4950906946375997881/1202240000\) \(29019150954560000\) \([2]\) \(1327104\) \(2.5362\)  
37570.b2 37570c1 \([1, 0, 1, -643754, -196195044]\) \(1222331589867961/18828492800\) \(454474044126003200\) \([2]\) \(663552\) \(2.1896\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37570.b have rank \(0\).

Complex multiplication

The elliptic curves in class 37570.b do not have complex multiplication.

Modular form 37570.2.a.b

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