Cremona's table of elliptic curves

3634 = 2 · 23 · 79

Field	Data	Notes
Atkin-Lehner	2- 23+ 79+	Signs for the Atkin-Lehner involutions
Class	3634d	Isogeny class
Conductor	3634	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	2912	Modular degree for the optimal curve
Δ	684703744 = 214 · 232 · 79	Discriminant
Eigenvalues	2- -1 -3 -5 -6  1 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-267,-1223]	[a1,a2,a3,a4,a6]
Generators	[-13:22:1] [-11:28:1]	Generators of the group modulo torsion
j	2105518942513/684703744	j-invariant
L	4.2228846055066	L(r)(E,1)/r!
Ω	1.211608361063	Real period
R	0.12447694501483	Regulator
r	2	Rank of the group of rational points
S	0.99999999999978	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	29072n1 116288e1 32706b1 90850d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3634d1

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
-	-1	-3	-5	-6	1	-6	-2	+	-2	-4	-2	6	-4	-7	4	5	-10	-12	5	-14	+	0	-5	15

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Quadratic twists for elliptic curve 3634d1

-4	8	-3	5	-23
29072n1	116288e1	32706b1	90850d1	83582o1

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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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