Cremona's table of elliptic curves

475 = 5² · 19

Field	Data	Notes
Atkin-Lehner	5+ 19-	Signs for the Atkin-Lehner involutions
Class	475a	Isogeny class
Conductor	475	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	36	Modular degree for the optimal curve
Δ	-296875 = -1 · 56 · 19	Discriminant
Eigenvalues	0  2 5+  1  3  4  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,17,-7]	[a1,a2,a3,a4,a6]
j	32768/19	j-invariant
L	1.8243091182881	L(r)(E,1)/r!
Ω	1.8243091182881	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7600m1 30400g1 4275k1 19a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 475a1

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	2	+	1	3	4	3	-	0	6	-4	-2	-6	1	3	-12	-6	-1	4	6	7	8	-12	12	-8

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Quadratic twists for elliptic curve 475a1

-4	8	-3	5	-7	-11	13	-19
7600m1	30400g1	4275k1	19a3	23275i1	57475h1	80275a1	9025c1

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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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