Cremona's table of elliptic curves

122304 = 2⁶ · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 13+	Signs for the Atkin-Lehner involutions
Class	122304da	Isogeny class
Conductor	122304	Conductor
∏ cp	152	Product of Tamagawa factors cp
deg	3502080	Modular degree for the optimal curve
Δ	-4.0774008304856E+20	Discriminant
Eigenvalues	2+ 3- -1 7-  1 13+  5  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2488481,1795502463]	[a1,a2,a3,a4,a6]
Generators	[331:31752:1]	Generators of the group modulo torsion
j	-442067613591752/105765793497	j-invariant
L	9.2007982924255	L(r)(E,1)/r!
Ω	0.1604636270317	Real period
R	0.37722921216119	Regulator
r	1	Rank of the group of rational points
S	1.0000000017781	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	122304s1 61152i1 17472k1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304da1

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
+	-	-1	-	1	+	5	3	7	5	4	-3	0	-5	0	6	-4	5	6	-8	-1	-10	-6	-14	18

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Quadratic twists for elliptic curve 122304da1

-4	8	-7
122304s1	61152i1	17472k1

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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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