Properties

Label 4573691.a
Number of curves $1$
Conductor $4573691$
CM no
Rank $4$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 4573691.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
4573691.a1 \([0, -1, 1, -72, 282]\) \(-41854210048/4573691\) \(-4573691\) \([]\) \(1928992\) \(0.015846\)

Rank

sage: E.rank()
 

The elliptic curve 4573691.a1 has rank \(4\).

Complex multiplication

The elliptic curves in class 4573691.a do not have complex multiplication.

Modular form 4573691.2.a.a

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