Properties

Label 413712bp
Number of curves $1$
Conductor $413712$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 413712bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
413712.bp1 413712bp1 \([0, 0, 0, -105456, 52552240]\) \(-53248/459\) \(-1118013326477438976\) \([]\) \(6289920\) \(2.1458\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 413712bp1 has rank \(1\).

Complex multiplication

The elliptic curves in class 413712bp do not have complex multiplication.

Modular form 413712.2.a.bp

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