Cremona's table of elliptic curves

8840 = 2³ · 5 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 5- 13- 17+	Signs for the Atkin-Lehner involutions
Class	8840b	Isogeny class
Conductor	8840	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	73548800 = 210 · 52 · 132 · 17	Discriminant
Eigenvalues	2+  0 5-  4 -2 13- 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-107,-106]	[a1,a2,a3,a4,a6]
Generators	[-2:10:1]	Generators of the group modulo torsion
j	132304644/71825	j-invariant
L	4.9254490731543	L(r)(E,1)/r!
Ω	1.583018907202	Real period
R	1.5557139118004	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	17680c1 70720a1 79560bn1 44200l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8840b1

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	-	+	-4	-2	0	0	-10	0	4	0	14	0	-8	-8	-16	-8	14	-8	-10	-8

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Quadratic twists for elliptic curve 8840b1

-4	8	-3	5	13
17680c1	70720a1	79560bn1	44200l1	114920k1

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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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