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	1824g	Isogeny class
Conductor	1824	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-6303744 = -1 · 212 · 34 · 19	Discriminant
Eigenvalues	2- 3+ -1 -1  3  0 -7 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,19,-123]	[a1,a2,a3,a4,a6]
Generators	[11:36:1]	Generators of the group modulo torsion
j	175616/1539	j-invariant
L	2.4030016210517	L(r)(E,1)/r!
Ω	1.1793914149138	Real period
R	0.50937322221126	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1824h1 3648bd1 5472k1 45600r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1824g1

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
-	+	-1	-1	3	0	-7	-	8	0	-2	4	-4	-1	-3	6	-6	-5	-2	-2	-11	-10	16	-14	-8

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Quadratic twists for elliptic curve 1824g1

-4	8	-3	5	-7	-19
1824h1	3648bd1	5472k1	45600r1	89376ck1	34656o1

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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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