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	16	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	1871424 = 26 · 34 · 192	Discriminant
Eigenvalues	2- 3- -2 -4  4  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-114,-504]	[a1,a2,a3,a4,a6]
Generators	[18:60:1]	Generators of the group modulo torsion
j	2582630848/29241	j-invariant
L	2.9627817524023	L(r)(E,1)/r!
Ω	1.4610110660035	Real period
R	2.0278982283871	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1824c1 3648h2 5472f1 45600c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1824i1

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 1824i1

-4	8	-3	5	-7	-19
1824c1	3648h2	5472f1	45600c1	89376bx1	34656j1

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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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