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	122304hg	Isogeny class
Conductor	122304	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-38986899416285184 = -1 · 217 · 34 · 710 · 13	Discriminant
Eigenvalues	2- 3-  2 7- -4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,79903,3857055]	[a1,a2,a3,a4,a6]
j	3658553134/2528253	j-invariant
L	1.8389334589136	L(r)(E,1)/r!
Ω	0.22986674533496	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	122304v3 30576k3 17472bx4	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304hg3

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	-	-4	+	-2	-4	4	-10	8	-2	-10	4	-8	6	8	2	-8	-8	-6	-8	-8	-2	-14

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Quadratic twists for elliptic curve 122304hg3

-4	8	-7
122304v3	30576k3	17472bx4

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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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