Properties

Label 35574.z
Number of curves $1$
Conductor $35574$
CM no
Rank $0$

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

Elliptic curves in class 35574.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35574.z1 35574be1 \([1, 0, 1, 3735146, 4390645928]\) \(228516153239/462422016\) \(-11661870758813110370304\) \([]\) \(2027520\) \(2.9186\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 35574.z1 has rank \(0\).

Complex multiplication

The elliptic curves in class 35574.z do not have complex multiplication.

Modular form 35574.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} + q^{12} + q^{13} - q^{15} + q^{16} - 3 q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display