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	10710h	Isogeny class
Conductor	10710	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	877135370454000 = 24 · 37 · 53 · 74 · 174	Discriminant
Eigenvalues	2+ 3- 5+ 7-  4 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-290655,-60224099]	[a1,a2,a3,a4,a6]
Generators	[-310:281:1]	Generators of the group modulo torsion
j	3725035528036823281/1203203526000	j-invariant
L	3.1674839384462	L(r)(E,1)/r!
Ω	0.2056190998231	Real period
R	0.96278870164886	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	85680du4 3570u3 53550dr4 74970bw4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10710h3

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
+	-	+	-	4	-6	+	0	-4	6	0	-6	6	-4	12	-6	4	-2	-4	0	2	4	0	10	2

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Quadratic twists for elliptic curve 10710h3

-4	-3	5	-7
85680du4	3570u3	53550dr4	74970bw4

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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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