Properties

Label 3643883.a
Number of curves $1$
Conductor $3643883$
CM no
Rank $4$

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

Elliptic curves in class 3643883.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
3643883.a1 \([0, 0, 1, -37, 126]\) \(-5601816576/3643883\) \(-3643883\) \([]\) \(3223536\) \(-0.039848\)

Rank

sage: E.rank()
 

The elliptic curve 3643883.a1 has rank \(4\).

Complex multiplication

The elliptic curves in class 3643883.a do not have complex multiplication.

Modular form 3643883.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - 3 q^{3} + 2 q^{4} - 4 q^{5} + 6 q^{6} - q^{7} + 6 q^{9} + 8 q^{10} - 2 q^{11} - 6 q^{12} - 2 q^{13} + 2 q^{14} + 12 q^{15} - 4 q^{16} - 5 q^{17} - 12 q^{18} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display