Properties

Label 59535.z
Number of curves $1$
Conductor $59535$
CM no
Rank $1$

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

Elliptic curves in class 59535.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59535.z1 59535r1 \([0, 0, 1, 11907, -145861]\) \(995328/625\) \(-117231566641875\) \([]\) \(248832\) \(1.3886\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 59535.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 59535.z do not have complex multiplication.

Modular form 59535.2.a.z

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} - q^{5} - 2 q^{10} + 2 q^{11} - q^{13} - 4 q^{16} - 2 q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display