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	122304dj	Isogeny class
Conductor	122304	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	10357671164166144 = 214 · 310 · 77 · 13	Discriminant
Eigenvalues	2+ 3- -2 7-  0 13+  4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-79249,-7080529]	[a1,a2,a3,a4,a6]
Generators	[-145:1176:1]	Generators of the group modulo torsion
j	28556329552/5373459	j-invariant
L	7.2044763158816	L(r)(E,1)/r!
Ω	0.28825157127739	Real period
R	0.62484275952254	Regulator
r	1	Rank of the group of rational points
S	1.0000000036831	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	122304fj2 7644c2 17472e2	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304dj2

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

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Quadratic twists for elliptic curve 122304dj2

-4	8	-7
122304fj2	7644c2	17472e2

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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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