Cremona's table of elliptic curves

12264 = 2³ · 3 · 7 · 73

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 73-	Signs for the Atkin-Lehner involutions
Class	12264f	Isogeny class
Conductor	12264	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	12771561269634048 = 210 · 320 · 72 · 73	Discriminant
Eigenvalues	2- 3+  2 7+  0 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-95992,-10041572]	[a1,a2,a3,a4,a6]
Generators	[-27770:64944:125]	Generators of the group modulo torsion
j	95528597284175332/12472227802377	j-invariant
L	4.1953963357818	L(r)(E,1)/r!
Ω	0.27356766359493	Real period
R	7.6679317296687	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	24528g3 98112v3 36792d3 85848u3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12264f3

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	+	0	-2	-2	-4	0	2	0	6	10	4	-4	2	0	-2	12	0	-	0	-16	2	18

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Quadratic twists for elliptic curve 12264f3

-4	8	-3	-7
24528g3	98112v3	36792d3	85848u3

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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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