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	6930bi	Isogeny class
Conductor	6930	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	-4903042134375000 = -1 · 23 · 37 · 58 · 72 · 114	Discriminant
Eigenvalues	2- 3- 5- 7- 11+ -6 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,42268,391839]	[a1,a2,a3,a4,a6]
Generators	[47:1551:1]	Generators of the group modulo torsion
j	11456208593737991/6725709375000	j-invariant
L	6.3797181674195	L(r)(E,1)/r!
Ω	0.262439983567	Real period
R	0.50644262870349	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	55440ej3 2310c4 34650m3 48510da3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6930bi4

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

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Quadratic twists for elliptic curve 6930bi4

-4	-3	5	-7	-11
55440ej3	2310c4	34650m3	48510da3	76230by3

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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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