Cremona's table of elliptic curves

69678 = 2 · 3² · 7² · 79

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 79-	Signs for the Atkin-Lehner involutions
Class	69678bg	Isogeny class
Conductor	69678	Conductor
∏ cp	288	Product of Tamagawa factors cp
Δ	1534475911391019072 = 26 · 310 · 77 · 793	Discriminant
Eigenvalues	2- 3-  0 7-  0  4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-31719155,-68751197805]	[a1,a2,a3,a4,a6]
Generators	[8885:587820:1]	Generators of the group modulo torsion
j	41150276566229265625/17891399232	j-invariant
L	10.912183709699	L(r)(E,1)/r!
Ω	0.063616411086797	Real period
R	2.3823743666163	Regulator
r	1	Rank of the group of rational points
S	1.000000000065	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	23226d3 9954k3	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 69678bg3

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	-	0	4	6	-2	0	0	-8	8	-6	-10	0	-12	12	10	8	-12	-2	-	-6	6	-14

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Quadratic twists for elliptic curve 69678bg3

-3	-7
23226d3	9954k3

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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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