Cremona's table of elliptic curves

475 = 5² · 19

Field	Data	Notes
Atkin-Lehner	5- 19-	Signs for the Atkin-Lehner involutions
Class	475c	Isogeny class
Conductor	475	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	45125 = 53 · 192	Discriminant
Eigenvalues	-1  0 5-  2 -4 -2  4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-25,52]	[a1,a2,a3,a4,a6]
Generators	[-2:10:1]	Generators of the group modulo torsion
j	13312053/361	j-invariant
L	1.3360934191063	L(r)(E,1)/r!
Ω	3.5833759752496	Real period
R	0.37285884270438	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	7600t2 30400s2 4275o2 475b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 475c2

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 475c2

-4	8	-3	5	-7	-11	13	-19
7600t2	30400s2	4275o2	475b2	23275ba2	57475k2	80275o2	9025g2

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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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