Properties

Label 45177.k
Number of curves $1$
Conductor $45177$
CM no
Rank $1$

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

Elliptic curves in class 45177.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
45177.k1 45177k1 \([1, 0, 1, -976126, 681881159]\) \(-21390625/29403\) \(-141386806302202014147\) \([]\) \(1332000\) \(2.5590\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 45177.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 45177.k do not have complex multiplication.

Modular form 45177.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{6} + 3 q^{7} - 3 q^{8} + q^{9} + q^{11} - q^{12} + 5 q^{13} + 3 q^{14} - q^{16} + 4 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display