Cremona's table of elliptic curves

11774 = 2 · 7 · 29²

Field	Data	Notes
Atkin-Lehner	2- 7- 29+	Signs for the Atkin-Lehner involutions
Class	11774l	Isogeny class
Conductor	11774	Conductor
∏ cp	320	Product of Tamagawa factors cp
deg	537600	Modular degree for the optimal curve
Δ	-5.5100319089528E+20	Discriminant
Eigenvalues	2- -2  2 7- -4 -2  4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1786722,-1456339388]	[a1,a2,a3,a4,a6]
Generators	[3318:169064:1]	Generators of the group modulo torsion
j	-1060490285861833/926330847232	j-invariant
L	5.4351131651043	L(r)(E,1)/r!
Ω	0.062988892833644	Real period
R	1.0785856284731	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	94192t1 105966x1 82418o1 406d1	Quadratic twists by: -4 -3 -7 29

Hecke Eigenvalues for elliptic curve 11774l1

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

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Quadratic twists for elliptic curve 11774l1

-4	-3	-7	29
94192t1	105966x1	82418o1	406d1

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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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