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	122304ik	Isogeny class
Conductor	122304	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	368640	Modular degree for the optimal curve
Δ	6345523993536 = 26 · 33 · 710 · 13	Discriminant
Eigenvalues	2- 3-  2 7- -4 13- -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-23732,1394070]	[a1,a2,a3,a4,a6]
Generators	[193:2010:1]	Generators of the group modulo torsion
j	196325547328/842751	j-invariant
L	10.032539693995	L(r)(E,1)/r!
Ω	0.75657837922062	Real period
R	4.4201367333423	Regulator
r	1	Rank of the group of rational points
S	1.0000000036937	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	122304gd1 61152e3 17472cg1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304ik1

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	-	-6	4	8	6	0	-10	10	8	0	-10	0	-2	-4	-12	-14	0	-16	10	2

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Quadratic twists for elliptic curve 122304ik1

-4	8	-7
122304gd1	61152e3	17472cg1

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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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