Cremona's table of elliptic curves

1974 = 2 · 3 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 47+	Signs for the Atkin-Lehner involutions
Class	1974h	Isogeny class
Conductor	1974	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	1625673882 = 2 · 3 · 78 · 47	Discriminant
Eigenvalues	2- 3- -2 7+  0 -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1554,23370]	[a1,a2,a3,a4,a6]
Generators	[1844:2417:64]	Generators of the group modulo torsion
j	415044078605857/1625673882	j-invariant
L	4.345766145788	L(r)(E,1)/r!
Ω	1.5067209180264	Real period
R	5.7685084129321	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	15792w3 63168a3 5922f3 49350h3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1974h4

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

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Quadratic twists for elliptic curve 1974h4

-4	8	-3	5	-7	-47
15792w3	63168a3	5922f3	49350h3	13818t3	92778u3

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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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