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	10710bg	Isogeny class
Conductor	10710	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	-252965916000000 = -1 · 28 · 312 · 56 · 7 · 17	Discriminant
Eigenvalues	2- 3- 5+ 7-  0 -4 17-  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-161978,-25062919]	[a1,a2,a3,a4,a6]
Generators	[627:10621:1]	Generators of the group modulo torsion
j	-644706081631626841/347004000000	j-invariant
L	6.478283689852	L(r)(E,1)/r!
Ω	0.1189848698835	Real period
R	3.4028925779572	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	85680dy1 3570n1 53550u1 74970di1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10710bg1

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

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Quadratic twists for elliptic curve 10710bg1

-4	-3	5	-7
85680dy1	3570n1	53550u1	74970di1

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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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