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	1974a	Isogeny class
Conductor	1974	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1282563072 = 210 · 34 · 7 · 472	Discriminant
Eigenvalues	2+ 3+  0 7+ -2 -4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-38220,-2891952]	[a1,a2,a3,a4,a6]
j	6174666627902151625/1282563072	j-invariant
L	0.682897315555	L(r)(E,1)/r!
Ω	0.3414486577775	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15792bd2 63168ba2 5922m2 49350ce2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1974a2

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	+	-2	-4	-2	0	6	2	4	-2	8	-6	-	2	12	10	-2	-16	-4	-8	4	-6	18

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Quadratic twists for elliptic curve 1974a2

-4	8	-3	5	-7	-47
15792bd2	63168ba2	5922m2	49350ce2	13818h2	92778a2

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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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