Cremona's table of elliptic curves

1824 = 2⁵ · 3 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 19+	Signs for the Atkin-Lehner involutions
Class	1824i	Isogeny class
Conductor	1824	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-600519168 = -1 · 29 · 32 · 194	Discriminant
Eigenvalues	2- 3- -2 -4  4  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-24,-1188]	[a1,a2,a3,a4,a6]
Generators	[138:495:8]	Generators of the group modulo torsion
j	-3112136/1172889	j-invariant
L	2.9627817524023	L(r)(E,1)/r!
Ω	0.73050553300173	Real period
R	4.0557964567741	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1824c4 3648h4 5472f4 45600c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1824i4

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

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Quadratic twists for elliptic curve 1824i4

-4	8	-3	5	-7	-19
1824c4	3648h4	5472f4	45600c2	89376bx2	34656j2

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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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