Properties

Label 205504.z
Number of curves $1$
Conductor $205504$
CM no
Rank $0$

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

Elliptic curves in class 205504.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
205504.z1 205504bw1 \([0, -1, 0, -5633, -231167]\) \(-31250/19\) \(-12020530675712\) \([]\) \(299520\) \(1.2119\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 205504.z1 has rank \(0\).

Complex multiplication

The elliptic curves in class 205504.z do not have complex multiplication.

Modular form 205504.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{7} - 2 q^{9} + 2 q^{11} - 5 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display