Cremona's table of elliptic curves

3410 = 2 · 5 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2- 5+ 11- 31-	Signs for the Atkin-Lehner involutions
Class	3410c	Isogeny class
Conductor	3410	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-21142000 = -1 · 24 · 53 · 11 · 312	Discriminant
Eigenvalues	2-  0 5+ -4 11- -2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-13,-219]	[a1,a2,a3,a4,a6]
j	-225866529/21142000	j-invariant
L	1.9048093293298	L(r)(E,1)/r!
Ω	0.9524046646649	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27280k1 109120k1 30690o1 17050e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3410c1

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	+	-4	-	-2	6	-2	8	0	-	-8	2	4	-2	0	0	8	10	8	-2	-4	12	14	-2

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Quadratic twists for elliptic curve 3410c1

-4	8	-3	5	-11	-31
27280k1	109120k1	30690o1	17050e1	37510d1	105710e1

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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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