Cremona's table of elliptic curves

1694 = 2 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 7- 11-	Signs for the Atkin-Lehner involutions
Class	1694j	Isogeny class
Conductor	1694	Conductor
∏ cp	45	Product of Tamagawa factors cp
deg	47520	Modular degree for the optimal curve
Δ	-223196311177731584 = -1 · 29 · 75 · 1110	Discriminant
Eigenvalues	2-  3  2 7- 11- -5 -8  3	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-127194,-28630247]	[a1,a2,a3,a4,a6]
j	-8773917273/8605184	j-invariant
L	5.4704558232399	L(r)(E,1)/r!
Ω	0.12156568496089	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13552u1 54208bq1 15246u1 42350q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1694j1

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
-	3	2	-	-	-5	-8	3	1	8	-8	-2	2	2	-4	12	-15	-10	0	-8	-4	3	-3	6	16

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Quadratic twists for elliptic curve 1694j1

-4	8	-3	5	-7	-11
13552u1	54208bq1	15246u1	42350q1	11858bp1	1694b1

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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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