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	122304ih	Isogeny class
Conductor	122304	Conductor
∏ cp	288	Product of Tamagawa factors cp
Δ	-5.540915901908E+24	Discriminant
Eigenvalues	2- 3-  2 7-  4 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-116085377,494512633215]	[a1,a2,a3,a4,a6]
Generators	[-6305:987840:1]	Generators of the group modulo torsion
j	-16354376146655191/523792501128	j-invariant
L	11.634315131545	L(r)(E,1)/r!
Ω	0.075784584087456	Real period
R	2.1321976090551	Regulator
r	1	Rank of the group of rational points
S	1.0000000072149	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	122304ca2 30576bt2 122304fm2	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304ih2

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	0	4	-4	0	8	-6	-4	-8	-14	-14	-16	10	8	-4	0	2

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Quadratic twists for elliptic curve 122304ih2

-4	8	-7
122304ca2	30576bt2	122304fm2

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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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