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	10710c	Isogeny class
Conductor	10710	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	10752	Modular degree for the optimal curve
Δ	-22298477040 = -1 · 24 · 39 · 5 · 72 · 172	Discriminant
Eigenvalues	2+ 3+ 5- 7+  2  6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-474,-8092]	[a1,a2,a3,a4,a6]
j	-599077107/1132880	j-invariant
L	1.9266448329767	L(r)(E,1)/r!
Ω	0.48166120824418	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	85680de1 10710q1 53550cv1 74970e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10710c1

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
+	+	-	+	2	6	+	-4	4	10	0	12	6	-6	-8	-2	0	-2	-2	6	12	-16	-4	12	4

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Quadratic twists for elliptic curve 10710c1

-4	-3	5	-7
85680de1	10710q1	53550cv1	74970e1

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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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