Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 75712.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.j1 75712bj1 \([0, 1, 0, -38081, -3786977]\) \(-114244/49\) \(-2619526698041344\) \([]\) \(399360\) \(1.6660\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.j1 has rank \(0\).

Complex multiplication

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

Modular form 75712.2.a.j

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} + q^{7} + q^{9} - 2 q^{11} + 2 q^{15} - 3 q^{17} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display