Cremona's table of elliptic curves

172 = 2² · 43

Field	Data	Notes
Atkin-Lehner	2- 43-	Signs for the Atkin-Lehner involutions
Class	172a	Isogeny class
Conductor	172	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-20353792 = -1 · 28 · 433	Discriminant
Eigenvalues	2- -2  0 -4 -3 -1 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,67,79]	[a1,a2,a3,a4,a6]
Generators	[10:43:1]	Generators of the group modulo torsion
j	128000000/79507	j-invariant
L	1.0159589214554	L(r)(E,1)/r!
Ω	1.3365424419992	Real period
R	0.25337988766889	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	688b2 2752b2 1548c2 4300b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 172a2

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
-	-2	0	-4	-3	-1	-3	2	-3	6	5	8	-3	-	-12	-9	-12	-10	11	6	-10	8	-15	0	-1

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Quadratic twists for elliptic curve 172a2

-4	8	-3	5	-7	-11	13	17	-19	-23	-43
688b2	2752b2	1548c2	4300b2	8428b2	20812i2	29068e2	49708c2	62092b2	90988e2	7396a2

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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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