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	5005d	Isogeny class
Conductor	5005	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	64320	Modular degree for the optimal curve
Δ	-44954964899499655 = -1 · 5 · 72 · 113 · 1310	Discriminant
Eigenvalues	-1  0 5- 7+ 11- 13-  6  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-866212,-310252794]	[a1,a2,a3,a4,a6]
j	-71877974412415806187281/44954964899499655	j-invariant
L	1.1736497682524	L(r)(E,1)/r!
Ω	0.078243317883496	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	80080bv1 45045p1 25025i1 35035e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5005d1

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

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Quadratic twists for elliptic curve 5005d1

-4	-3	5	-7	-11	13
80080bv1	45045p1	25025i1	35035e1	55055r1	65065i1

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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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