Properties

Label 476850.z
Number of curves $1$
Conductor $476850$
CM no
Rank $1$

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

Elliptic curves in class 476850.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
476850.z1 476850z1 \([1, 1, 0, -69071150, -220978353000]\) \(-334350814467169/16500\) \(-1798437465257812500\) \([]\) \(45826560\) \(2.9781\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 476850.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 476850.z do not have complex multiplication.

Modular form 476850.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 2 q^{7} - q^{8} + q^{9} + q^{11} - q^{12} + 2 q^{13} + 2 q^{14} + q^{16} - q^{18} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display