Cremona's table of elliptic curves

6720 = 2⁶ · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7+	Signs for the Atkin-Lehner involutions
Class	6720bg	Isogeny class
Conductor	6720	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	825753600 = 219 · 32 · 52 · 7	Discriminant
Eigenvalues	2- 3+ 5+ 7+  4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1075201,429482401]	[a1,a2,a3,a4,a6]
j	524388516989299201/3150	j-invariant
L	1.5453737168316	L(r)(E,1)/r!
Ω	0.77268685841582	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6720u5 1680t5 20160ev5 33600gt6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720bg5

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

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Quadratic twists for elliptic curve 6720bg5

-4	8	-3	5	-7
6720u5	1680t5	20160ev5	33600gt6	47040hc6

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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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