Cremona's table of elliptic curves

6930 = 2 · 3² · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	6930g	Isogeny class
Conductor	6930	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	830300767203600 = 24 · 310 · 52 · 74 · 114	Discriminant
Eigenvalues	2+ 3- 5+ 7+ 11- -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-29205,1337125]	[a1,a2,a3,a4,a6]
Generators	[-82:1823:1]	Generators of the group modulo torsion
j	3778993806976081/1138958528400	j-invariant
L	2.7268656790033	L(r)(E,1)/r!
Ω	0.46517310774813	Real period
R	0.732755621935	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	55440dl3 2310n3 34650dn3 48510bu3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6930g4

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	6	-4	0	2	-8	6	6	-4	-8	2	4	-2	-4	0	10	-16	-4	6	10

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Quadratic twists for elliptic curve 6930g4

-4	-3	5	-7	-11
55440dl3	2310n3	34650dn3	48510bu3	76230dw3

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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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