Properties

Label 351975by
Number of curves $1$
Conductor $351975$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 351975by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
351975.by1 351975by1 \([0, 1, 1, -598658, 279884219]\) \(-32278933504/27421875\) \(-20157597938232421875\) \([]\) \(13208832\) \(2.4018\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 351975by1 has rank \(1\).

Complex multiplication

The elliptic curves in class 351975by do not have complex multiplication.

Modular form 351975.2.a.by

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