Cremona's table of elliptic curves

4182 = 2 · 3 · 17 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 17+ 41+	Signs for the Atkin-Lehner involutions
Class	4182f	Isogeny class
Conductor	4182	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	-1259216928 = -1 · 25 · 34 · 172 · 412	Discriminant
Eigenvalues	2- 3+ -4 -4 -4 -4 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,40,1721]	[a1,a2,a3,a4,a6]
Generators	[-9:31:1] [-7:37:1]	Generators of the group modulo torsion
j	7066834559/1259216928	j-invariant
L	4.402836260146	L(r)(E,1)/r!
Ω	1.181887394289	Real period
R	0.37252586679761	Regulator
r	2	Rank of the group of rational points
S	0.99999999999984	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	33456t2 12546g2 104550bb2 71094bb2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 4182f2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	+	-4	-4	-4	-4	+	-8	-2	-6	2	-8	+	4	-6	0	-12	-8	8	12	-6	8	4	-6	-6

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Quadratic twists for elliptic curve 4182f2

-4	-3	5	17
33456t2	12546g2	104550bb2	71094bb2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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