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	122304bi	Isogeny class
Conductor	122304	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	675840	Modular degree for the optimal curve
Δ	-2526928665870336 = -1 · 215 · 3 · 711 · 13	Discriminant
Eigenvalues	2+ 3+ -3 7-  3 13+ -1  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-22017,2733249]	[a1,a2,a3,a4,a6]
j	-306182024/655473	j-invariant
L	1.6247152720157	L(r)(E,1)/r!
Ω	0.40617898582253	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	122304du1 61152cf1 17472bl1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304bi1

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
+	+	-3	-	3	+	-1	3	5	3	8	5	-12	7	-8	2	0	1	-14	-4	11	6	6	-10	10

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Quadratic twists for elliptic curve 122304bi1

-4	8	-7
122304du1	61152cf1	17472bl1

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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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