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	4182a	Isogeny class
Conductor	4182	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-8466974623872 = -1 · 27 · 34 · 172 · 414	Discriminant
Eigenvalues	2+ 3+  0 -2  0 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-4675,-188339]	[a1,a2,a3,a4,a6]
Generators	[85:151:1]	Generators of the group modulo torsion
j	-11303519856765625/8466974623872	j-invariant
L	2.1031101568153	L(r)(E,1)/r!
Ω	0.2795694517036	Real period
R	3.7613375567318	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	33456p2 12546n2 104550ce2 71094j2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 4182a2

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
+	+	0	-2	0	-2	+	4	2	4	-2	8	+	4	0	-6	4	8	4	-6	-6	-14	4	6	-2

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Quadratic twists for elliptic curve 4182a2

-4	-3	5	17
33456p2	12546n2	104550ce2	71094j2

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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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