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	16	Product of Tamagawa factors cp
deg	16640	Modular degree for the optimal curve
Δ	-5410205689392 = -1 · 24 · 35 · 72 · 734	Discriminant
Eigenvalues	2- 3+  2 7+  0 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2193,103968]	[a1,a2,a3,a4,a6]
Generators	[2993:163735:1]	Generators of the group modulo torsion
j	72865436813312/338137855587	j-invariant
L	4.1953963357818	L(r)(E,1)/r!
Ω	0.54713532718987	Real period
R	7.6679317296687	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	24528g1 98112v1 36792d1 85848u1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12264f1

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 12264f1

-4	8	-3	-7
24528g1	98112v1	36792d1	85848u1

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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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