Properties

Label 248773b
Number of curves $1$
Conductor $248773$
CM no
Rank $1$

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

Elliptic curves in class 248773b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248773.b1 248773b1 \([0, -1, 1, -54112, -4826606]\) \(148944426176512/12189877\) \(1434126839173\) \([]\) \(1176576\) \(1.3774\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 248773b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 248773b do not have complex multiplication.

Modular form 248773.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{9} - 4 q^{10} + 6 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display