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	1974d	Isogeny class
Conductor	1974	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-5264989632 = -1 · 26 · 36 · 74 · 47	Discriminant
Eigenvalues	2- 3+  2 7+ -2 -4 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-3527,79229]	[a1,a2,a3,a4,a6]
Generators	[29:34:1]	Generators of the group modulo torsion
j	-4852301599161073/5264989632	j-invariant
L	3.9035341185328	L(r)(E,1)/r!
Ω	1.3541236610885	Real period
R	0.48045022655648	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	15792bg1 63168bg1 5922d1 49350bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1974d1

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

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Quadratic twists for elliptic curve 1974d1

-4	8	-3	5	-7	-47
15792bg1	63168bg1	5922d1	49350bc1	13818bd1	92778n1

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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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