Properties

Label 38646.k
Number of curves $1$
Conductor $38646$
CM no
Rank $0$

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

Elliptic curves in class 38646.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38646.k1 38646i1 \([1, -1, 0, 27, 243]\) \(2924207/38646\) \(-28172934\) \([]\) \(12160\) \(0.11027\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 38646.k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 38646.k do not have complex multiplication.

Modular form 38646.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} + 3 q^{7} - q^{8} - 3 q^{10} - 2 q^{13} - 3 q^{14} + q^{16} + 4 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display