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	122304ff	Isogeny class
Conductor	122304	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1179648	Modular degree for the optimal curve
Δ	383436131339072448 = 26 · 316 · 77 · 132	Discriminant
Eigenvalues	2- 3+  2 7-  0 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-184452,6552162]	[a1,a2,a3,a4,a6]
Generators	[-104687:6036212:1331]	Generators of the group modulo torsion
j	92173898928448/50924270943	j-invariant
L	7.5788185938352	L(r)(E,1)/r!
Ω	0.26108581284425	Real period
R	7.257018810738	Regulator
r	1	Rank of the group of rational points
S	0.99999999653309	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	122304hf1 61152cc3 17472dd1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304ff1

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

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Quadratic twists for elliptic curve 122304ff1

-4	8	-7
122304hf1	61152cc3	17472dd1

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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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