Cremona's table of elliptic curves

8740 = 2² · 5 · 19 · 23

Field	Data	Notes
Atkin-Lehner	2- 5- 19+ 23+	Signs for the Atkin-Lehner involutions
Class	8740c	Isogeny class
Conductor	8740	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	10627840 = 28 · 5 · 192 · 23	Discriminant
Eigenvalues	2-  0 5-  0 -4  4 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-607,-5754]	[a1,a2,a3,a4,a6]
Generators	[35:126:1]	Generators of the group modulo torsion
j	96616170576/41515	j-invariant
L	4.2882340855916	L(r)(E,1)/r!
Ω	0.96186380314785	Real period
R	2.9721699832885	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	34960k2 78660j2 43700e2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 8740c2

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	-	0	-4	4	-2	+	+	2	2	2	6	8	8	-6	10	-2	-14	-6	-10	16	-12	8	-2

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Quadratic twists for elliptic curve 8740c2

-4	-3	5
34960k2	78660j2	43700e2

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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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