Cremona's table of elliptic curves

12078 = 2 · 3² · 11 · 61

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 61+	Signs for the Atkin-Lehner involutions
Class	12078q	Isogeny class
Conductor	12078	Conductor
∏ cp	256	Product of Tamagawa factors cp
deg	307200	Modular degree for the optimal curve
Δ	-7.5500830591411E+19	Discriminant
Eigenvalues	2- 3+  0 -2 11- -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-87455,-418152185]	[a1,a2,a3,a4,a6]
Generators	[1811:72310:1]	Generators of the group modulo torsion
j	-3758215647796875/3835839587024896	j-invariant
L	6.6327631559461	L(r)(E,1)/r!
Ω	0.087391841427745	Real period
R	1.1858878657151	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	96624r1 12078a1	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 12078q1

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
-	+	0	-2	-	-2	-2	4	8	-6	2	2	-12	-2	4	-2	-4	+	-2	-16	-6	10	4	-6	-2

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Quadratic twists for elliptic curve 12078q1

-4	-3
96624r1	12078a1

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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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