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	474b	Isogeny class
Conductor	474	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	40	Modular degree for the optimal curve
Δ	-76788 = -1 · 22 · 35 · 79	Discriminant
Eigenvalues	2+ 3- -2 -1 -5 -1 -1 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-7,14]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	-30664297/76788	j-invariant
L	1.5313917146814	L(r)(E,1)/r!
Ω	3.0414875397006	Real period
R	0.050350090036278	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	3792d1 15168b1 1422h1 11850w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 474b1

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	-1	-5	-1	-1	-2	-5	1	0	4	-6	1	4	-2	-6	0	-10	6	7	-	-15	4	-1

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Quadratic twists for elliptic curve 474b1

-4	8	-3	5	-7	-11	13	-79
3792d1	15168b1	1422h1	11850w1	23226g1	57354x1	80106bj1	37446c1

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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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