Properties

Label 5712f
Number of curves $1$
Conductor $5712$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 5712f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5712.h1 5712f1 \([0, -1, 0, 679, -159051]\) \(135037162496/42645837339\) \(-10917334358784\) \([]\) \(8448\) \(1.1809\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5712f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5712f do not have complex multiplication.

Modular form 5712.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + 3 q^{11} + q^{13} + q^{15} + q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display