Cremona's table of elliptic curves

1764 = 2² · 3² · 7²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7-	Signs for the Atkin-Lehner involutions
Class	1764b	Isogeny class
Conductor	1764	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	592815428352 = 28 · 39 · 76	Discriminant
Eigenvalues	2- 3+  0 7-  0 -2  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6615,203742]	[a1,a2,a3,a4,a6]
Generators	[-66:594:1]	Generators of the group modulo torsion
j	54000	j-invariant
L	2.9019616070319	L(r)(E,1)/r!
Ω	0.91794366225235	Real period
R	3.1613722348836	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	7056bf4 28224i4 1764b2 44100e4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1764b4

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	-	0	-2	0	-8	0	0	4	-10	0	8	0	0	0	-14	-16	0	10	-4	0	0	-14

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Quadratic twists for elliptic curve 1764b4

-4	8	-3	5	-7
7056bf4	28224i4	1764b2	44100e4	36a4

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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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