Cremona's table of elliptic curves

474 = 2 · 3 · 79

Field	Data	Notes
Atkin-Lehner	2+ 3+ 79+	Signs for the Atkin-Lehner involutions
Class	474a	Isogeny class
Conductor	474	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	-34947072 = -1 · 214 · 33 · 79	Discriminant
Eigenvalues	2+ 3+  2 -3 -5 -1  5 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,81,-27]	[a1,a2,a3,a4,a6]
Generators	[14:57:1]	Generators of the group modulo torsion
j	57646656647/34947072	j-invariant
L	1.3453488048479	L(r)(E,1)/r!
Ω	1.1990226569707	Real period
R	0.56101892529993	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3792f1 15168f1 1422g1 11850bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 474a1

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	-3	-5	-1	5	-6	3	-5	-4	-8	-2	-5	0	2	-2	-12	14	10	-9	+	9	-12	7

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Quadratic twists for elliptic curve 474a1

-4	8	-3	5	-7	-11	13	-79
3792f1	15168f1	1422g1	11850bb1	23226l1	57354s1	80106s1	37446g1

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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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