Cremona's table of elliptic curves

122694 = 2 · 3 · 11² · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 13+	Signs for the Atkin-Lehner involutions
Class	122694cz	Isogeny class
Conductor	122694	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	196992	Modular degree for the optimal curve
Δ	-189230220036 = -1 · 22 · 34 · 112 · 136	Discriminant
Eigenvalues	2- 3-  1  4 11- 13+ -7  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2285,46773]	[a1,a2,a3,a4,a6]
j	-2259169/324	j-invariant
L	7.8049317393095	L(r)(E,1)/r!
Ω	0.97561657932833	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	122694bg1 726d1	Quadratic twists by: -11 13

Hecke Eigenvalues for elliptic curve 122694cz1

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
-	-	1	4	-	+	-7	0	0	-7	8	5	11	8	-4	-5	0	2	-12	16	-6	-4	-8	17	5

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Quadratic twists for elliptic curve 122694cz1

-11	13
122694bg1	726d1

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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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