Properties

Label 374790.f
Number of curves $1$
Conductor $374790$
CM no
Rank $1$

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

Elliptic curves in class 374790.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
374790.f1 374790f1 \([1, 1, 0, -95603663, 744372532917]\) \(-117904499185849/223842949200\) \(-183468013005526459618309200\) \([]\) \(138086400\) \(3.7293\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 374790.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 374790.f do not have complex multiplication.

Modular form 374790.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + 3 q^{11} - q^{12} + q^{13} + q^{14} + q^{15} + q^{16} + 6 q^{17} - q^{18} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display