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	4	Product of Tamagawa factors cp
Δ	705078125 = 59 · 192	Discriminant
Eigenvalues	1  0 5- -2 -4  2 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-617,5916]	[a1,a2,a3,a4,a6]
Generators	[8:34:1]	Generators of the group modulo torsion
j	13312053/361	j-invariant
L	2.1875734113977	L(r)(E,1)/r!
Ω	1.6025344539195	Real period
R	1.3650710635564	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	7600s2 30400t2 4275q2 475c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 475b2

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 475b2

-4	8	-3	5	-7	-11	13	-19
7600s2	30400t2	4275q2	475c2	23275y2	57475l2	80275s2	9025h2

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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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