Cremona's table of elliptic curves

747 = 3² · 83

Field	Data	Notes
Atkin-Lehner	3+ 83+	Signs for the Atkin-Lehner involutions
Class	747a	Isogeny class
Conductor	747	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	135596187 = 39 · 832	Discriminant
Eigenvalues	-1 3+ -2  0  0  6 -4  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-191,892]	[a1,a2,a3,a4,a6]
Generators	[-10:46:1]	Generators of the group modulo torsion
j	38958219/6889	j-invariant
L	1.4144734402638	L(r)(E,1)/r!
Ω	1.7571979728231	Real period
R	0.80495963581799	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	11952j2 47808e2 747b2 18675c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 747a2

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
-1	+	-2	0	0	6	-4	2	-4	-4	-4	-2	-8	-2	0	6	-4	2	-14	8	6	2	+	-6	-2

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Quadratic twists for elliptic curve 747a2

-4	8	-3	5	-7	-11	13	-83
11952j2	47808e2	747b2	18675c2	36603b2	90387d2	126243e2	62001c2

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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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