Properties

Label 37.a
Number of curves $1$
Conductor $37$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 37.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37.a1 37a1 \([0, 0, 1, -1, 0]\) \(110592/37\) \(37\) \([]\) \(2\) \(-0.99654\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 37.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 37.a do not have complex multiplication.

Modular form 37.2.a.a

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