Properties

Label 37570.f
Number of curves $1$
Conductor $37570$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 37570.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37570.f1 37570l1 \([1, 0, 0, -6, -20]\) \(-83521/520\) \(-150280\) \([]\) \(4752\) \(-0.32304\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 37570.f1 has rank \(1\).

Complex multiplication

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

Modular form 37570.2.a.f

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