Properties

Label 75712.bg
Number of curves $1$
Conductor $75712$
CM no
Rank $0$

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75712.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.bg1 75712u1 \([0, 0, 0, -4394, -742586]\) \(-13824/343\) \(-232789970236096\) \([]\) \(179712\) \(1.4374\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.bg1 has rank \(0\).

Complex multiplication

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

Modular form 75712.2.a.bg

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