Properties

Label 5712.m
Number of curves $1$
Conductor $5712$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 5712.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5712.m1 5712h1 \([0, -1, 0, -89, 357]\) \(-307981312/2499\) \(-639744\) \([]\) \(1280\) \(-0.058546\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5712.m1 has rank \(1\).

Complex multiplication

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

Modular form 5712.2.a.m

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