Cremona's table of elliptic curves

10764 = 2² · 3² · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 23-	Signs for the Atkin-Lehner involutions
Class	10764c	Isogeny class
Conductor	10764	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	326890107648 = 28 · 33 · 132 · 234	Discriminant
Eigenvalues	2- 3+  0  0  4 13+  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2175,-27706]	[a1,a2,a3,a4,a6]
Generators	[-37:46:1]	Generators of the group modulo torsion
j	164625750000/47293129	j-invariant
L	4.7853200319555	L(r)(E,1)/r!
Ω	0.71440541283122	Real period
R	0.55819379608177	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	43056r2 10764a2	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 10764c2

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	4	+	4	-4	-	0	-4	6	-4	-4	-12	-4	12	-10	-4	-12	6	8	-12	8	6

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Quadratic twists for elliptic curve 10764c2

-4	-3
43056r2	10764a2

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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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