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	32	Product of Tamagawa factors cp
deg	1327104	Modular degree for the optimal curve
Δ	4940285273565808068 = 22 · 318 · 79 · 79	Discriminant
Eigenvalues	2- 3-  0 7-  0  4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-463280,-57285777]	[a1,a2,a3,a4,a6]
Generators	[-64897772:1740362727:314432]	Generators of the group modulo torsion
j	128214670515625/57601827108	j-invariant
L	10.912183709699	L(r)(E,1)/r!
Ω	0.19084923326039	Real period
R	7.1471230998488	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	23226d1 9954k1	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 69678bg1

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 69678bg1

-3	-7
23226d1	9954k1

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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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