Properties

Label 75712bu
Number of curves $1$
Conductor $75712$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 75712bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.be1 75712bu1 \([0, 0, 0, 676, 2704]\) \(73008/49\) \(-22929227776\) \([]\) \(46080\) \(0.67669\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712bu1 has rank \(2\).

Complex multiplication

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

Modular form 75712.2.a.bu

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