Cremona's table of elliptic curves

6708 = 2² · 3 · 13 · 43

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 43-	Signs for the Atkin-Lehner involutions
Class	6708c	Isogeny class
Conductor	6708	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	684461995776 = 28 · 314 · 13 · 43	Discriminant
Eigenvalues	2- 3+  2  0  0 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2252,11160]	[a1,a2,a3,a4,a6]
Generators	[54:210:1]	Generators of the group modulo torsion
j	4936074881488/2673679671	j-invariant
L	3.956230402691	L(r)(E,1)/r!
Ω	0.79073416234737	Real period
R	3.3354913202406	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	26832p2 107328w2 20124e2 87204k2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6708c2

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

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Quadratic twists for elliptic curve 6708c2

-4	8	-3	13
26832p2	107328w2	20124e2	87204k2

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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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