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	1694i	Isogeny class
Conductor	1694	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	3819485516 = 22 · 72 · 117	Discriminant
Eigenvalues	2-  2  2 7- 11-  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-28377,1828091]	[a1,a2,a3,a4,a6]
j	1426487591593/2156	j-invariant
L	4.7561194926712	L(r)(E,1)/r!
Ω	1.1890298731678	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13552r2 54208bo2 15246s2 42350o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1694i2

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	-	-	4	0	-4	4	-2	-10	-6	0	4	10	-14	10	8	8	-4	-4	-16	-4	10	6

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Quadratic twists for elliptic curve 1694i2

-4	8	-3	5	-7	-11
13552r2	54208bo2	15246s2	42350o2	11858bm2	154c2

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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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