Cremona's table of elliptic curves

10710 = 2 · 3² · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7- 17+	Signs for the Atkin-Lehner involutions
Class	10710bk	Isogeny class
Conductor	10710	Conductor
∏ cp	432	Product of Tamagawa factors cp
Δ	594873815256000 = 26 · 37 · 53 · 76 · 172	Discriminant
Eigenvalues	2- 3- 5- 7-  0 -4 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1150907,475521131]	[a1,a2,a3,a4,a6]
Generators	[-839:29574:1]	Generators of the group modulo torsion
j	231268521845235080809/816013464000	j-invariant
L	7.3196668304117	L(r)(E,1)/r!
Ω	0.45149859984845	Real period
R	1.350994745216	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	85680et4 3570k4 53550ba4 74970cu4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10710bk4

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	+	2	-6	0	-4	-4	-6	-4	-6	-6	0	2	-4	-12	2	2	6	-12	14

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Quadratic twists for elliptic curve 10710bk4

-4	-3	5	-7
85680et4	3570k4	53550ba4	74970cu4

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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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