Properties

Label 177600.z
Number of curves $1$
Conductor $177600$
CM no
Rank $1$

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

Elliptic curves in class 177600.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177600.z1 177600if1 \([0, -1, 0, -420033, 169559937]\) \(-16006818542408/14955044985\) \(-7656983032320000000\) \([]\) \(3502080\) \(2.3200\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177600.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 177600.z do not have complex multiplication.

Modular form 177600.2.a.z

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