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	122304fh	Isogeny class
Conductor	122304	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	7.4917238913967E+22	Discriminant
Eigenvalues	2- 3+  2 7-  4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-10621697,-2024516703]	[a1,a2,a3,a4,a6]
Generators	[2241594736008630436977487:-177022059201965505095271880:292679953994278595737]	Generators of the group modulo torsion
j	8594236719188066/4858291807551	j-invariant
L	7.1843127918594	L(r)(E,1)/r!
Ω	0.090149211870901	Real period
R	39.84678680364	Regulator
r	1	Rank of the group of rational points
S	0.99999999164673	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	122304di4 30576bd4 17472ct3	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304fh4

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

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Quadratic twists for elliptic curve 122304fh4

-4	8	-7
122304di4	30576bd4	17472ct3

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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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