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	1974c	Isogeny class
Conductor	1974	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-768160655474688 = -1 · 224 · 32 · 72 · 473	Discriminant
Eigenvalues	2+ 3-  0 7- -6 -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,9909,-1277450]	[a1,a2,a3,a4,a6]
Generators	[982:10215:8]	Generators of the group modulo torsion
j	107615839766636375/768160655474688	j-invariant
L	2.6135596215192	L(r)(E,1)/r!
Ω	0.25131373183685	Real period
R	5.1997946996702	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	15792r3 63168s3 5922q3 49350bq3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1974c3

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

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Quadratic twists for elliptic curve 1974c3

-4	8	-3	5	-7	-47
15792r3	63168s3	5922q3	49350bq3	13818e3	92778h3

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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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