Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75712.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.bf1 75712d1 \([0, 0, 0, -394784, 95683744]\) \(-86044336128/218491\) \(-17278801104388096\) \([]\) \(645120\) \(1.9925\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.bf1 has rank \(1\).

Complex multiplication

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

Modular form 75712.2.a.bf

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