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	69678s	Isogeny class
Conductor	69678	Conductor
∏ cp	126	Product of Tamagawa factors cp
Δ	-2982460469175936 = -1 · 27 · 39 · 74 · 793	Discriminant
Eigenvalues	2- 3+ -3 7+  0 -4  3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-88724,-10483721]	[a1,a2,a3,a4,a6]
Generators	[1549:-60499:1]	Generators of the group modulo torsion
j	-1634402470491/63108992	j-invariant
L	7.0366863939277	L(r)(E,1)/r!
Ω	0.13799940947844	Real period
R	0.40468808973838	Regulator
r	1	Rank of the group of rational points
S	1.0000000000944	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69678b1 69678u2	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 69678s2

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	+	0	-4	3	-1	0	0	-10	11	-3	2	-6	0	12	5	5	6	-10	-	6	-12	2

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Quadratic twists for elliptic curve 69678s2

-3	-7
69678b1	69678u2

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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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