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	10710m	Isogeny class
Conductor	10710	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	139479342187500 = 22 · 37 · 58 · 74 · 17	Discriminant
Eigenvalues	2+ 3- 5- 7-  0 -2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-15534,486040]	[a1,a2,a3,a4,a6]
Generators	[-114:932:1]	Generators of the group modulo torsion
j	568671957006049/191329687500	j-invariant
L	3.7304510193263	L(r)(E,1)/r!
Ω	0.53580417826521	Real period
R	0.43514626829298	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	85680ff3 3570r3 53550dh3 74970o3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10710m4

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

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Quadratic twists for elliptic curve 10710m4

-4	-3	5	-7
85680ff3	3570r3	53550dh3	74970o3

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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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