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	3410b	Isogeny class
Conductor	3410	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	352	Modular degree for the optimal curve
Δ	-426250 = -1 · 2 · 54 · 11 · 31	Discriminant
Eigenvalues	2-  0 5+  1 11+ -4  1  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-13,-33]	[a1,a2,a3,a4,a6]
Generators	[54:69:8]	Generators of the group modulo torsion
j	-225866529/426250	j-invariant
L	4.6883218071223	L(r)(E,1)/r!
Ω	1.1910168951651	Real period
R	1.9682012178645	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	27280m1 109120p1 30690s1 17050a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3410b1

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	+	1	+	-4	1	2	3	0	-	-3	6	-11	-12	-2	-15	-14	7	-10	-6	2	-15	2	13

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Quadratic twists for elliptic curve 3410b1

-4	8	-3	5	-11	-31
27280m1	109120p1	30690s1	17050a1	37510c1	105710h1

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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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