Properties

Label 409101by
Number of curves $1$
Conductor $409101$
CM no
Rank $0$

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

Elliptic curves in class 409101by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
409101.by1 409101by1 \([1, 0, 1, 73180, -13255189]\) \(1268071343/2956581\) \(-101054475453803949\) \([]\) \(3477600\) \(1.9469\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101by1 has rank \(0\).

Complex multiplication

The elliptic curves in class 409101by do not have complex multiplication.

Modular form 409101.2.a.by

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