Properties

Label 409101.bi
Number of curves $1$
Conductor $409101$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 409101.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
409101.bi1 409101bi1 \([1, 1, 0, -338990698, 2402218755721]\) \(-1411796061716161/31236921\) \(-95319841363772517852129\) \([]\) \(75018240\) \(3.5245\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101.bi1 has rank \(1\).

Complex multiplication

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

Modular form 409101.2.a.bi

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