Properties

Label 40080.q
Number of curves $1$
Conductor $40080$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 40080.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40080.q1 40080h1 \([0, -1, 0, -120, -225]\) \(12043745536/5072625\) \(81162000\) \([]\) \(13440\) \(0.21454\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40080.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 40080.q do not have complex multiplication.

Modular form 40080.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 2 q^{7} + q^{9} - 4 q^{11} + q^{13} - q^{15} + 8 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display