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	1764k	Isogeny class
Conductor	1764	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-201721916592 = -1 · 24 · 37 · 78	Discriminant
Eigenvalues	2- 3-  4 7- -2  6 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-588,-22295]	[a1,a2,a3,a4,a6]
j	-16384/147	j-invariant
L	2.5465032069302	L(r)(E,1)/r!
Ω	0.42441720115503	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	7056cb1 28224cu1 588f1 44100bz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1764k1

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
-	-	4	-	-2	6	-4	4	-2	2	0	2	0	-4	12	6	-8	-6	-8	-14	2	12	-4	0	2

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Quadratic twists for elliptic curve 1764k1

-4	8	-3	5	-7
7056cb1	28224cu1	588f1	44100bz1	252b1

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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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