Cremona's table of elliptic curves

5005 = 5 · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	5- 7+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	5005b	Isogeny class
Conductor	5005	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	29570556640625 = 512 · 7 · 113 · 13	Discriminant
Eigenvalues	1  0 5- 7+ 11+ 13+ -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-646304,200149235]	[a1,a2,a3,a4,a6]
j	29856206199428401347801/29570556640625	j-invariant
L	1.6668300854059	L(r)(E,1)/r!
Ω	0.55561002846862	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	80080bx4 45045r4 25025h4 35035c4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5005b4

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
1	0	-	+	+	+	-2	8	0	-2	0	2	-6	-4	-8	6	-4	2	0	16	14	-12	12	-6	10

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Quadratic twists for elliptic curve 5005b4

-4	-3	5	-7	-11	13
80080bx4	45045r4	25025h4	35035c4	55055u4	65065m4

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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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