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	1694f	Isogeny class
Conductor	1694	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	173612978 = 2 · 72 · 116	Discriminant
Eigenvalues	2- -2  0 7+ 11-  4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1273,-17577]	[a1,a2,a3,a4,a6]
Generators	[806:7099:8]	Generators of the group modulo torsion
j	128787625/98	j-invariant
L	3.0275445242376	L(r)(E,1)/r!
Ω	0.79930129180543	Real period
R	3.7877388104793	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	13552ba2 54208m2 15246i2 42350bb2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1694f2

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	+	-	4	-6	-2	0	6	-4	2	-6	-8	-12	6	-6	-8	-4	0	-2	-8	6	-6	-10

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Quadratic twists for elliptic curve 1694f2

-4	8	-3	5	-7	-11
13552ba2	54208m2	15246i2	42350bb2	11858bk2	14a6

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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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