Cremona's table of elliptic curves

684 = 2² · 3² · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 19+	Signs for the Atkin-Lehner involutions
Class	684b	Isogeny class
Conductor	684	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	2584929024 = 28 · 312 · 19	Discriminant
Eigenvalues	2- 3- -2  0 -2  2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-831,-8890]	[a1,a2,a3,a4,a6]
Generators	[-17:18:1]	Generators of the group modulo torsion
j	340062928/13851	j-invariant
L	2.0174937497296	L(r)(E,1)/r!
Ω	0.89143385110214	Real period
R	0.75440024601387	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	2736u2 10944bf2 228a2 17100m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 684b2

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	0	-2	2	-6	+	-2	-4	-8	-2	8	-8	-2	4	0	2	12	4	6	-16	-6	0	-2

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Quadratic twists for elliptic curve 684b2

-4	8	-3	5	-7	-11	13	-19
2736u2	10944bf2	228a2	17100m2	33516v2	82764n2	115596w2	12996o2

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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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