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	122304ij	Isogeny class
Conductor	122304	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	3424741744976068608 = 222 · 35 · 76 · 134	Discriminant
Eigenvalues	2- 3-  2 7- -4 13- -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-65039137,201866191967]	[a1,a2,a3,a4,a6]
Generators	[4007:74880:1]	Generators of the group modulo torsion
j	986551739719628473/111045168	j-invariant
L	10.218403976844	L(r)(E,1)/r!
Ω	0.19382265347218	Real period
R	1.3180095095227	Regulator
r	1	Rank of the group of rational points
S	0.99999999602232	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	122304by4 30576br4 2496u3	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304ij4

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

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Quadratic twists for elliptic curve 122304ij4

-4	8	-7
122304by4	30576br4	2496u3

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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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