Cremona's table of elliptic curves

17680 = 2⁴ · 5 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 5- 13- 17-	Signs for the Atkin-Lehner involutions
Class	17680o	Isogeny class
Conductor	17680	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-361345254400000000 = -1 · 216 · 58 · 132 · 174	Discriminant
Eigenvalues	2-  0 5-  4  0 13- 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,170533,10086026]	[a1,a2,a3,a4,a6]
Generators	[10:3434:1]	Generators of the group modulo torsion
j	133902615693854799/88219056250000	j-invariant
L	6.0376838366109	L(r)(E,1)/r!
Ω	0.18938326932723	Real period
R	3.9850958443026	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2210g4 70720bc3 88400s3	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 17680o4

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	-	4	0	-	-	4	-4	-10	-4	-10	2	4	8	-10	12	-10	4	-12	-14	-4	-4	-6	10

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Quadratic twists for elliptic curve 17680o4

-4	8	5
2210g4	70720bc3	88400s3

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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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