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	1694c	Isogeny class
Conductor	1694	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-18593344 = -1 · 26 · 74 · 112	Discriminant
Eigenvalues	2+  0 -1 7- 11-  1  1  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-50,-236]	[a1,a2,a3,a4,a6]
Generators	[12:22:1]	Generators of the group modulo torsion
j	-115538049/153664	j-invariant
L	2.0648055331932	L(r)(E,1)/r!
Ω	0.85474854009077	Real period
R	0.30196096225182	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13552l1 54208bc1 15246bq1 42350bs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1694c1

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
+	0	-1	-	-	1	1	0	4	5	-8	-5	5	-4	-4	-9	-12	2	0	4	-10	-12	12	15	-17

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Quadratic twists for elliptic curve 1694c1

-4	8	-3	5	-7	-11
13552l1	54208bc1	15246bq1	42350bs1	11858h1	1694e1

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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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