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	5005a	Isogeny class
Conductor	5005	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	5268935546875 = 510 · 73 · 112 · 13	Discriminant
Eigenvalues	1  0 5+ 7- 11+ 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-23065,-1337994]	[a1,a2,a3,a4,a6]
j	1357046347029907689/5268935546875	j-invariant
L	1.1624732939538	L(r)(E,1)/r!
Ω	0.38749109798461	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	80080w2 45045br2 25025a2 35035j2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5005a2

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

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Quadratic twists for elliptic curve 5005a2

-4	-3	5	-7	-11	13
80080w2	45045br2	25025a2	35035j2	55055d2	65065s2

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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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