Cremona's table of elliptic curves

13300 = 2² · 5² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 19-	Signs for the Atkin-Lehner involutions
Class	13300s	Isogeny class
Conductor	13300	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	1459808000 = 28 · 53 · 74 · 19	Discriminant
Eigenvalues	2- -2 5- 7+ -4 -6  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-588,-5372]	[a1,a2,a3,a4,a6]
Generators	[-16:14:1] [-12:10:1]	Generators of the group modulo torsion
j	703791632/45619	j-invariant
L	4.6715780832876	L(r)(E,1)/r!
Ω	0.97332221649305	Real period
R	1.5998737807919	Regulator
r	2	Rank of the group of rational points
S	0.99999999999979	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53200dt2 119700by2 13300x2 93100bq2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13300s2

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

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Quadratic twists for elliptic curve 13300s2

-4	-3	5	-7
53200dt2	119700by2	13300x2	93100bq2

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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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