Cremona's table of elliptic curves

1704 = 2³ · 3 · 71

Field	Data	Notes
Atkin-Lehner	2+ 3+ 71+	Signs for the Atkin-Lehner involutions
Class	1704a	Isogeny class
Conductor	1704	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	30971904 = 211 · 3 · 712	Discriminant
Eigenvalues	2+ 3+ -2 -2  2  4 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-104,-276]	[a1,a2,a3,a4,a6]
Generators	[13:20:1]	Generators of the group modulo torsion
j	61328594/15123	j-invariant
L	2.2076623003244	L(r)(E,1)/r!
Ω	1.5207334820619	Real period
R	2.9034177603969	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	3408d2 13632i2 5112d2 42600bc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1704a2

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	-2	2	4	-4	4	4	-6	2	2	-4	-4	0	-2	-6	-12	-12	+	10	0	0	-18	2

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Quadratic twists for elliptic curve 1704a2

-4	8	-3	5	-7	-71
3408d2	13632i2	5112d2	42600bc2	83496g2	120984b2

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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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