Properties

Label 86394.e
Number of curves $1$
Conductor $86394$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 86394.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86394.e1 86394k1 \([1, 1, 0, -266, -1866]\) \(-17303415217/983178\) \(-118964538\) \([]\) \(34560\) \(0.30649\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 86394.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 86394.e do not have complex multiplication.

Modular form 86394.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 2 q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + 2 q^{10} - q^{12} - 5 q^{13} - q^{14} + 2 q^{15} + q^{16} - q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display