Cremona's table of elliptic curves

121968 = 2⁴ · 3² · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 11-	Signs for the Atkin-Lehner involutions
Class	121968gf	Isogeny class
Conductor	121968	Conductor
∏ cp	120	Product of Tamagawa factors cp
Δ	-2.9136049846748E+25	Discriminant
Eigenvalues	2- 3-  3 7- 11-  7 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,65315679,-161752020397]	[a1,a2,a3,a4,a6]
Generators	[929962:896838327:1]	Generators of the group modulo torsion
j	1491325446082364672/1410025768453071	j-invariant
L	10.376383015919	L(r)(E,1)/r!
Ω	0.036236169106661	Real period
R	2.3862858551357	Regulator
r	1	Rank of the group of rational points
S	1.0000000078925	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	30492s2 40656by2 11088bn2	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 121968gf2

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	-	-	7	-6	-1	0	-3	-2	5	-12	8	-3	12	-3	10	13	-12	-11	8	-6	-6	8

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Quadratic twists for elliptic curve 121968gf2

-4	-3	-11
30492s2	40656by2	11088bn2

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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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