Properties

Label 17787.z
Number of curves $1$
Conductor $17787$
CM no
Rank $0$

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

Elliptic curves in class 17787.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17787.z1 17787c1 \([0, -1, 1, 69172, -25440955]\) \(3584000/29403\) \(-300283918846086483\) \([]\) \(302400\) \(2.0350\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 17787.z1 has rank \(0\).

Complex multiplication

The elliptic curves in class 17787.z do not have complex multiplication.

Modular form 17787.2.a.z

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{6} + q^{9} - 2 q^{12} + 5 q^{13} - 4 q^{16} - 6 q^{17} + 2 q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display