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
deg	336	Modular degree for the optimal curve
Δ	164944 = 24 · 132 · 61	Discriminant
Eigenvalues	2-  0 -2  4  4 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-16,-15]	[a1,a2,a3,a4,a6]
Generators	[-2:3:1]	Generators of the group modulo torsion
j	28311552/10309	j-invariant
L	3.3323076314609	L(r)(E,1)/r!
Ω	2.459764914805	Real period
R	0.90315070663979	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	12688f1 50752b1 28548f1 79300b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3172b1

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 3172b1

-4	8	-3	5	13
12688f1	50752b1	28548f1	79300b1	41236a1

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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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