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	3400c	Isogeny class
Conductor	3400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-4624000000 = -1 · 210 · 56 · 172	Discriminant
Eigenvalues	2+  2 5+  2 -6 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,392,1212]	[a1,a2,a3,a4,a6]
Generators	[42:300:1]	Generators of the group modulo torsion
j	415292/289	j-invariant
L	4.6523260200912	L(r)(E,1)/r!
Ω	0.86918320885661	Real period
R	1.3381315851152	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	6800d2 27200n2 30600ci2 136a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3400c2

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	+	2	-6	-2	+	0	-6	-10	2	-6	-6	8	0	10	-8	14	-4	2	14	-10	-8	-10	-2

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Quadratic twists for elliptic curve 3400c2

-4	8	-3	5	17
6800d2	27200n2	30600ci2	136a2	57800h2

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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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