Properties

Label 6045.b
Number of curves $1$
Conductor $6045$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 6045.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6045.b1 6045d1 \([0, -1, 1, 10, 68]\) \(99897344/2266875\) \(-2266875\) \([]\) \(1600\) \(-0.10025\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6045.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6045.b do not have complex multiplication.

Modular form 6045.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + 2 q^{7} + q^{9} - 2 q^{10} - 5 q^{11} - 2 q^{12} - q^{13} - 4 q^{14} - q^{15} - 4 q^{16} + 4 q^{17} - 2 q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display