Properties

Label 185020.a
Number of curves $1$
Conductor $185020$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 185020.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185020.a1 185020a1 \([0, 0, 0, -232, 11281]\) \(-102629376/4026275\) \(-54177556400\) \([]\) \(216000\) \(0.73979\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 185020.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 185020.a do not have complex multiplication.

Modular form 185020.2.a.a

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