Properties

Label 340032.a
Number of curves $1$
Conductor $340032$
CM no
Rank $0$

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

Elliptic curves in class 340032.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
340032.a1 340032a1 \([0, -1, 0, -81025, 41632801]\) \(-224412099736609/2722801160772\) \(-713765987489415168\) \([]\) \(6580224\) \(2.1076\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 340032.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 340032.a do not have complex multiplication.

Modular form 340032.2.a.a

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