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Properties

Label 4592017.a
Number of curves $1$
Conductor $4592017$
CM no
Rank $4$

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

Rank

Copy content sage:E.rank()
 

The elliptic curve 4592017.a1 has rank \(4\).

Complex multiplication

The elliptic curves in class 4592017.a do not have complex multiplication.

Modular form 4592017.2.a.a

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

Elliptic curves in class 4592017.a

Copy content sage:E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
4592017.a1 \([1, -1, 1, -42, 0]\) \(8012006001/4592017\) \(4592017\) \([]\) \(3070544\) \(-0.031995\)