Cremona's table of elliptic curves

19380 = 2² · 3 · 5 · 17 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 17+ 19-	Signs for the Atkin-Lehner involutions
Class	19380i	Isogeny class
Conductor	19380	Conductor
∏ cp	432	Product of Tamagawa factors cp
Δ	6742076503622400 = 28 · 312 · 52 · 172 · 193	Discriminant
Eigenvalues	2- 3- 5+ -4 -6 -4 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-57236,3469764]	[a1,a2,a3,a4,a6]
Generators	[-260:918:1] [-233:2052:1]	Generators of the group modulo torsion
j	81002637420061264/26336236342275	j-invariant
L	7.2922437830911	L(r)(E,1)/r!
Ω	0.38875494666943	Real period
R	1.5631620565359	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	77520be2 58140t2 96900l2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 19380i2

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

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Quadratic twists for elliptic curve 19380i2

-4	-3	5
77520be2	58140t2	96900l2

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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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