Cremona's table of elliptic curves

1700 = 2² · 5² · 17

Field	Data	Notes
Atkin-Lehner	2- 5- 17+	Signs for the Atkin-Lehner involutions
Class	1700c	Isogeny class
Conductor	1700	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-491300000000 = -1 · 28 · 58 · 173	Discriminant
Eigenvalues	2-  1 5- -1  0 -1 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4708,-130412]	[a1,a2,a3,a4,a6]
Generators	[975387:6887672:9261]	Generators of the group modulo torsion
j	-115431760/4913	j-invariant
L	3.1820663644471	L(r)(E,1)/r!
Ω	0.28745668887815	Real period
R	11.06972454482	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	6800v2 27200bf2 15300bg2 1700b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1700c2

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
-	1	-	-1	0	-1	+	-4	0	-6	-1	2	0	2	-6	3	-6	-10	-4	-3	2	-1	12	-6	8

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Quadratic twists for elliptic curve 1700c2

-4	8	-3	5	-7	17
6800v2	27200bf2	15300bg2	1700b2	83300bk2	28900i2

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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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