Properties

Label 37180.f
Number of curves $1$
Conductor $37180$
CM no
Rank $1$

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

Elliptic curves in class 37180.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37180.f1 37180c1 \([0, -1, 0, -5126, 148745]\) \(-1141504/55\) \(-717843034480\) \([]\) \(59904\) \(1.0371\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 37180.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 37180.f do not have complex multiplication.

Modular form 37180.2.a.f

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - q^{5} - 4 q^{7} + q^{9} + q^{11} - 2 q^{15} - q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display