Cremona's table of elliptic curves

3434 = 2 · 17 · 101

Field	Data	Notes
Atkin-Lehner	2- 17- 101+	Signs for the Atkin-Lehner involutions
Class	3434b	Isogeny class
Conductor	3434	Conductor
∏ cp	72	Product of Tamagawa factors cp
deg	3744	Modular degree for the optimal curve
Δ	205281333248 = 212 · 173 · 1012	Discriminant
Eigenvalues	2- -2  2 -2 -2 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2257,34857]	[a1,a2,a3,a4,a6]
Generators	[-22:283:1]	Generators of the group modulo torsion
j	1271541138628753/205281333248	j-invariant
L	3.858734915448	L(r)(E,1)/r!
Ω	0.9580288194311	Real period
R	0.2237658801294	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	27472l1 109888l1 30906f1 85850b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3434b1

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	-2	-2	-2	-	4	4	-4	0	-2	-4	4	-8	-14	4	-8	-4	4	-4	-12	8	14	2

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Quadratic twists for elliptic curve 3434b1

-4	8	-3	5	17
27472l1	109888l1	30906f1	85850b1	58378i1

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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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