Properties

Label 75712.bk
Number of curves $1$
Conductor $75712$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 75712.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.bk1 75712cm1 \([0, 0, 0, -394784, -95683744]\) \(-86044336128/218491\) \(-17278801104388096\) \([]\) \(645120\) \(1.9925\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.bk1 has rank \(1\).

Complex multiplication

The elliptic curves in class 75712.bk do not have complex multiplication.

Modular form 75712.2.a.bk

sage: E.q_eigenform(10)
 
\(q - 3 q^{5} + q^{7} - 3 q^{9} + 2 q^{11} - 4 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display