Cremona's table of elliptic curves

3400 = 2³ · 5² · 17

Field	Data	Notes
Atkin-Lehner	2+ 5+ 17+	Signs for the Atkin-Lehner involutions
Class	3400a	Isogeny class
Conductor	3400	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-212500000000000 = -1 · 211 · 514 · 17	Discriminant
Eigenvalues	2+  0 5+  0  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,12925,414750]	[a1,a2,a3,a4,a6]
Generators	[-17514:219142:729]	Generators of the group modulo torsion
j	7462174302/6640625	j-invariant
L	3.3811224306402	L(r)(E,1)/r!
Ω	0.36615954395076	Real period
R	9.2340142063724	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	6800a4 27200a3 30600ch3 680a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3400a4

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	+	0	0	2	+	-4	8	2	-8	-2	2	4	0	-6	-4	-6	-4	-8	-2	0	-4	-6	-18

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Quadratic twists for elliptic curve 3400a4

-4	8	-3	5	17
6800a4	27200a3	30600ch3	680a4	57800a3

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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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