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	5005c	Isogeny class
Conductor	5005	Conductor
∏ cp	162	Product of Tamagawa factors cp
deg	178848	Modular degree for the optimal curve
Δ	-1.437473071859E+20	Discriminant
Eigenvalues	-2  0 5- 7+ 11- 13+ -5  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1111907,732397750]	[a1,a2,a3,a4,a6]
Generators	[-437:33687:1]	Generators of the group modulo torsion
j	-152029933359345706438656/143747307185904296875	j-invariant
L	1.8689897377799	L(r)(E,1)/r!
Ω	0.16746369752462	Real period
R	0.068892385994901	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	80080bs1 45045n1 25025l1 35035h1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5005c1

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
-2	0	-	+	-	+	-5	5	-6	4	6	5	3	-1	7	0	-10	-10	3	10	-4	-6	6	-6	7

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Quadratic twists for elliptic curve 5005c1

-4	-3	5	-7	-11	13
80080bs1	45045n1	25025l1	35035h1	55055v1	65065k1

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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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