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	5005f	Isogeny class
Conductor	5005	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	11616	Modular degree for the optimal curve
Δ	-1716715 = -1 · 5 · 74 · 11 · 13	Discriminant
Eigenvalues	-2  0 5- 7- 11- 13+ -5 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-74567,-7837330]	[a1,a2,a3,a4,a6]
j	-45852574428123549696/1716715	j-invariant
L	0.57782041604648	L(r)(E,1)/r!
Ω	0.14445510401162	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	80080bk1 45045bc1 25025d1 35035g1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5005f1

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	-3	-6	4	-10	-3	-5	7	-9	0	6	6	11	10	-4	10	6	10	7

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Quadratic twists for elliptic curve 5005f1

-4	-3	5	-7	-11	13
80080bk1	45045bc1	25025d1	35035g1	55055l1	65065d1

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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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