Properties

Label 164730.k
Number of curves $1$
Conductor $164730$
CM no
Rank $0$

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

Elliptic curves in class 164730.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
164730.k1 164730dh1 \([1, 1, 0, -294063, -107024283]\) \(-1394947801/1641600\) \(-3309455586977078400\) \([]\) \(4112640\) \(2.2476\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 164730.k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 164730.k do not have complex multiplication.

Modular form 164730.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} + 2 q^{11} - q^{12} + 7 q^{13} + q^{15} + q^{16} - q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display