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	36	Product of Tamagawa factors cp
Δ	44444922368 = 29 · 72 · 116	Discriminant
Eigenvalues	2- -2  0 7+ 11-  4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-330393,73068601]	[a1,a2,a3,a4,a6]
Generators	[362:-1149:1]	Generators of the group modulo torsion
j	2251439055699625/25088	j-invariant
L	3.0275445242376	L(r)(E,1)/r!
Ω	0.79930129180543	Real period
R	0.42085986783103	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	13552ba6 54208m6 15246i6 42350bb6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1694f6

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 1694f6

-4	8	-3	5	-7	-11
13552ba6	54208m6	15246i6	42350bb6	11858bk6	14a5

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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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