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	10710n	Isogeny class
Conductor	10710	Conductor
∏ cp	384	Product of Tamagawa factors cp
Δ	35692428915360000 = 28 · 38 · 54 · 76 · 172	Discriminant
Eigenvalues	2+ 3- 5- 7-  0 -2 17- -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-83259,1719013]	[a1,a2,a3,a4,a6]
Generators	[-163:3389:1]	Generators of the group modulo torsion
j	87557366190249649/48960807840000	j-invariant
L	3.5627198168512	L(r)(E,1)/r!
Ω	0.31702601390842	Real period
R	0.46824756494067	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	85680fh2 3570s2 53550di2 74970p2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10710n2

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

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Quadratic twists for elliptic curve 10710n2

-4	-3	5	-7
85680fh2	3570s2	53550di2	74970p2

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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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