Cremona's table of elliptic curves

19824 = 2⁴ · 3 · 7 · 59

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 59-	Signs for the Atkin-Lehner involutions
Class	19824d	Isogeny class
Conductor	19824	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	9403727864832 = 210 · 33 · 78 · 59	Discriminant
Eigenvalues	2+ 3+ -2 7- -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-34784,-2481072]	[a1,a2,a3,a4,a6]
Generators	[-104:28:1]	Generators of the group modulo torsion
j	4545428263979908/9183327993	j-invariant
L	3.1846795294204	L(r)(E,1)/r!
Ω	0.34962811323273	Real period
R	1.138595342053	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	9912g4 79296cg4 59472p4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 19824d3

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

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Quadratic twists for elliptic curve 19824d3

-4	8	-3
9912g4	79296cg4	59472p4

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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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