Cremona's table of elliptic curves

3172 = 2² · 13 · 61

Field	Data	Notes
Atkin-Lehner	2- 13- 61+	Signs for the Atkin-Lehner involutions
Class	3172b	Isogeny class
Conductor	3172	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-12383488 = -1 · 28 · 13 · 612	Discriminant
Eigenvalues	2-  0 -2  4  4 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,49,-106]	[a1,a2,a3,a4,a6]
Generators	[11:42:1]	Generators of the group modulo torsion
j	50824368/48373	j-invariant
L	3.3323076314609	L(r)(E,1)/r!
Ω	1.2298824574025	Real period
R	1.8063014132796	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	12688f2 50752b2 28548f2 79300b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3172b2

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	4	4	-	-6	-4	-6	6	-4	4	6	-6	-8	-14	8	+	8	8	-2	-6	-12	12	2

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Quadratic twists for elliptic curve 3172b2

-4	8	-3	5	13
12688f2	50752b2	28548f2	79300b2	41236a2

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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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