Cremona's table of elliptic curves

475 = 5² · 19

Field	Data	Notes
Atkin-Lehner	5- 19-	Signs for the Atkin-Lehner involutions
Class	475b	Isogeny class
Conductor	475	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-37109375 = -1 · 59 · 19	Discriminant
Eigenvalues	1  0 5- -2 -4  2 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,8,291]	[a1,a2,a3,a4,a6]
Generators	[10:31:1]	Generators of the group modulo torsion
j	27/19	j-invariant
L	2.1875734113977	L(r)(E,1)/r!
Ω	1.6025344539195	Real period
R	2.7301421271128	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	7600s1 30400t1 4275q1 475c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 475b1

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	0	-	-2	-4	2	-4	-	6	-6	-4	10	-10	-2	6	-10	0	2	-8	4	-4	4	18	-2	-6

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Quadratic twists for elliptic curve 475b1

-4	8	-3	5	-7	-11	13	-19
7600s1	30400t1	4275q1	475c1	23275y1	57475l1	80275s1	9025h1

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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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