Properties

Label 75504cz
Number of curves $1$
Conductor $75504$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cz1")
 
E.isogeny_class()
 

Elliptic curves in class 75504cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75504.co1 75504cz1 \([0, 1, 0, -117, 867]\) \(-360448/507\) \(-251277312\) \([]\) \(27648\) \(0.30412\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75504cz1 has rank \(1\).

Complex multiplication

The elliptic curves in class 75504cz do not have complex multiplication.

Modular form 75504.2.a.cz

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