Properties

Label 187395.z
Number of curves $1$
Conductor $187395$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 187395.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187395.z1 187395bc1 \([0, -1, 1, -63746, 9753251]\) \(-32278933504/27421875\) \(-24337015002421875\) \([]\) \(2570400\) \(1.8418\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 187395.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 187395.z do not have complex multiplication.

Modular form 187395.2.a.z

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - q^{7} + q^{9} - 2 q^{10} - 5 q^{11} - 2 q^{12} + q^{13} - 2 q^{14} + q^{15} - 4 q^{16} + 7 q^{17} + 2 q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display