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	1824j	Isogeny class
Conductor	1824	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-1663488 = -1 · 29 · 32 · 192	Discriminant
Eigenvalues	2- 3-  0  0  0  0 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8,60]	[a1,a2,a3,a4,a6]
j	-125000/3249	j-invariant
L	2.2285243414458	L(r)(E,1)/r!
Ω	2.2285243414458	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	1824a2 3648a2 5472i2 45600e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1824j2

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

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Quadratic twists for elliptic curve 1824j2

-4	8	-3	5	-7	-19
1824a2	3648a2	5472i2	45600e2	89376bi2	34656d2

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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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