Properties

Label 398502.f
Number of curves $1$
Conductor $398502$
CM no
Rank $0$

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

Elliptic curves in class 398502.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
398502.f1 398502f1 \([1, -1, 0, -25128, -3412044]\) \(-498677257/1145988\) \(-4032438125180868\) \([]\) \(2757888\) \(1.6829\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 398502.f1 has rank \(0\).

Complex multiplication

The elliptic curves in class 398502.f do not have complex multiplication.

Modular form 398502.2.a.f

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