Properties

Label 5850.j
Number of curves $1$
Conductor $5850$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 5850.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.j1 5850o1 \([1, -1, 0, 18, -284]\) \(34295/1872\) \(-34117200\) \([]\) \(1536\) \(0.12512\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5850.j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5850.j do not have complex multiplication.

Modular form 5850.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} + 3 q^{11} + q^{13} + q^{14} + q^{16} + q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display