Properties

Label 49686bj
Number of curves $1$
Conductor $49686$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 49686bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49686.bc1 49686bj1 \([1, 0, 1, -405942, -50977496]\) \(77086633/32928\) \(3160096985573822112\) \([]\) \(898560\) \(2.2463\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 49686bj1 has rank \(1\).

Complex multiplication

The elliptic curves in class 49686bj do not have complex multiplication.

Modular form 49686.2.a.bj

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} - q^{8} + q^{9} + 2 q^{10} - q^{11} + q^{12} - 2 q^{15} + q^{16} + q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display