Properties

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

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Show commands: SageMath
E = EllipticCurve("fn1")
 
E.isogeny_class()
 

Elliptic curves in class 340032.fn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
340032.fn1 340032fn1 \([0, 1, 0, -7425, -2440449]\) \(-172715635009/9694992384\) \(-2541484083511296\) \([]\) \(1351680\) \(1.6358\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 340032.fn1 has rank \(1\).

Complex multiplication

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

Modular form 340032.2.a.fn

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