Properties

Label 409101.bb
Number of curves $1$
Conductor $409101$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 409101.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
409101.bb1 409101bb1 \([0, 1, 1, -821, 8894]\) \(-134217728/1863\) \(-850520979\) \([]\) \(141312\) \(0.51967\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101.bb1 has rank \(2\).

Complex multiplication

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

Modular form 409101.2.a.bb

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