Properties

Label 18032k
Number of curves $1$
Conductor $18032$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 18032k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18032.i1 18032k1 \([0, -1, 0, -212, 1303]\) \(-562432/23\) \(-43294832\) \([]\) \(4608\) \(0.23284\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 18032k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 18032k do not have complex multiplication.

Modular form 18032.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} - 2 q^{9} + 2 q^{11} - 7 q^{13} - 2 q^{15} + 4 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display