Cremona's table of elliptic curves

15708 = 2² · 3 · 7 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 11+ 17-	Signs for the Atkin-Lehner involutions
Class	15708i	Isogeny class
Conductor	15708	Conductor
∏ cp	108	Product of Tamagawa factors cp
deg	31104	Modular degree for the optimal curve
Δ	21678626570832 = 24 · 36 · 7 · 11 · 176	Discriminant
Eigenvalues	2- 3-  0 7- 11+  2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-17073,-834624]	[a1,a2,a3,a4,a6]
Generators	[465:9591:1]	Generators of the group modulo torsion
j	34400019417088000/1354914160677	j-invariant
L	6.1726355101091	L(r)(E,1)/r!
Ω	0.41867102054942	Real period
R	4.9144676107179	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	62832z1 47124s1 109956g1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 15708i1

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	-	-4	0	0	-4	2	-6	-10	6	6	-6	14	-4	0	2	8	-12	-18	-4

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Quadratic twists for elliptic curve 15708i1

-4	-3	-7
62832z1	47124s1	109956g1

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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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