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	6720bq	Isogeny class
Conductor	6720	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1024	Modular degree for the optimal curve
Δ	-2903040 = -1 · 210 · 34 · 5 · 7	Discriminant
Eigenvalues	2- 3+ 5- 7+ -4 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,35,-35]	[a1,a2,a3,a4,a6]
Generators	[17:72:1]	Generators of the group modulo torsion
j	4499456/2835	j-invariant
L	3.3540441887379	L(r)(E,1)/r!
Ω	1.4609230985589	Real period
R	2.2958389747183	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	6720bd1 1680f1 20160dv1 33600gw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720bq1

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

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Quadratic twists for elliptic curve 6720bq1

-4	8	-3	5	-7
6720bd1	1680f1	20160dv1	33600gw1	47040gi1

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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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