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
deg	3584	Modular degree for the optimal curve
Δ	4213850112 = 214 · 32 · 17 · 412	Discriminant
Eigenvalues	2+ 3+  0 -2  0 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-5315,-151347]	[a1,a2,a3,a4,a6]
Generators	[-43:23:1]	Generators of the group modulo torsion
j	16609676962173625/4213850112	j-invariant
L	2.1031101568153	L(r)(E,1)/r!
Ω	0.5591389034072	Real period
R	1.8806687783659	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	33456p1 12546n1 104550ce1 71094j1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 4182a1

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 4182a1

-4	-3	5	17
33456p1	12546n1	104550ce1	71094j1

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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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