Cremona's table of elliptic curves

1952 = 2⁵ · 61

Field	Data	Notes
Atkin-Lehner	2+ 61+	Signs for the Atkin-Lehner involutions
Class	1952a	Isogeny class
Conductor	1952	Conductor
∏ cp	2	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	[7:12:1]	Generators of the group modulo torsion
j	-140608/61	j-invariant
L	3.5033198146053	L(r)(E,1)/r!
Ω	1.1457204071335	Real period
R	1.5288720497571	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	1952b1 3904e1 17568j1 48800j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1952a1

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 1952a1

-4	8	-3	5	-7	61
1952b1	3904e1	17568j1	48800j1	95648l1	119072f1

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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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