Cremona's table of elliptic curves

1952 = 2⁵ · 61

Field	Data	Notes
Atkin-Lehner	2- 61+	Signs for the Atkin-Lehner involutions
Class	1952b	Isogeny class
Conductor	1952	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-249856 = -1 · 212 · 61	Discriminant
Eigenvalues	2- -2 -3 -1 -3 -7 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-17,31]	[a1,a2,a3,a4,a6]
Generators	[-5:4:1] [1:4:1]	Generators of the group modulo torsion
j	-140608/61	j-invariant
L	2.3608239464244	L(r)(E,1)/r!
Ω	2.9181060247185	Real period
R	0.202256525845	Regulator
r	2	Rank of the group of rational points
S	0.99999999999862	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1952a1 3904d1 17568c1 48800b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1952b1

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	-3	-1	-3	-7	-4	-4	1	-6	0	-4	-3	8	-12	-2	-9	+	7	0	-11	-3	8	16	2

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Quadratic twists for elliptic curve 1952b1

-4	8	-3	5	-7	61
1952a1	3904d1	17568c1	48800b1	95648t1	119072d1

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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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