Cremona's table of elliptic curves

6992 = 2⁴ · 19 · 23

Field	Data	Notes
Atkin-Lehner	2- 19- 23+	Signs for the Atkin-Lehner involutions
Class	6992r	Isogeny class
Conductor	6992	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1600	Modular degree for the optimal curve
Δ	-41168896 = -1 · 212 · 19 · 232	Discriminant
Eigenvalues	2- -2  1  3 -5 -2  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5,307]	[a1,a2,a3,a4,a6]
Generators	[6:23:1]	Generators of the group modulo torsion
j	-4096/10051	j-invariant
L	3.1553034479661	L(r)(E,1)/r!
Ω	1.6374486461017	Real period
R	0.96348165039493	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	437b1 27968bf1 62928bo1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 6992r1

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	1	3	-5	-2	3	-	+	4	4	-8	0	3	3	12	-4	5	-12	-12	1	10	-12	-6	10

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Quadratic twists for elliptic curve 6992r1

-4	8	-3
437b1	27968bf1	62928bo1

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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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