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
deg	1536	Modular degree for the optimal curve
Δ	1700000000 = 28 · 58 · 17	Discriminant
Eigenvalues	2+  0 5+  0  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3575,82250]	[a1,a2,a3,a4,a6]
Generators	[-65:200:1]	Generators of the group modulo torsion
j	1263257424/425	j-invariant
L	3.3811224306402	L(r)(E,1)/r!
Ω	1.4646381758031	Real period
R	2.3085035515931	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	6800a1 27200a1 30600ch1 680a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3400a1

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 3400a1

-4	8	-3	5	17
6800a1	27200a1	30600ch1	680a1	57800a1

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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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