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	144	Product of Tamagawa factors cp
Δ	6442654991472 = 24 · 312 · 73 · 472	Discriminant
Eigenvalues	2+ 3-  0 7- -6 -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-28556,1850906]	[a1,a2,a3,a4,a6]
Generators	[-75:1927:1]	Generators of the group modulo torsion
j	2575099233338829625/6442654991472	j-invariant
L	2.6135596215192	L(r)(E,1)/r!
Ω	0.75394119551055	Real period
R	0.86663244994503	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	15792r2 63168s2 5922q2 49350bq2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1974c2

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 1974c2

-4	8	-3	5	-7	-47
15792r2	63168s2	5922q2	49350bq2	13818e2	92778h2

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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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