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	1824k	Isogeny class
Conductor	1824	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	224	Modular degree for the optimal curve
Δ	-69312 = -1 · 26 · 3 · 192	Discriminant
Eigenvalues	2- 3-  2  4 -6 -2  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2,12]	[a1,a2,a3,a4,a6]
j	-21952/1083	j-invariant
L	2.8759222860609	L(r)(E,1)/r!
Ω	2.8759222860609	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	1824f1 3648w2 5472m1 45600h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1824k1

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

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Quadratic twists for elliptic curve 1824k1

-4	8	-3	5	-7	-19
1824f1	3648w2	5472m1	45600h1	89376bn1	34656i1

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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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