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	2	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-2375 = -1 · 53 · 19	Discriminant
Eigenvalues	-1  0 5-  2 -4 -2  4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,0,2]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	27/19	j-invariant
L	1.3360934191063	L(r)(E,1)/r!
Ω	3.5833759752496	Real period
R	0.74571768540877	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	7600t1 30400s1 4275o1 475b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 475c1

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 475c1

-4	8	-3	5	-7	-11	13	-19
7600t1	30400s1	4275o1	475b1	23275ba1	57475k1	80275o1	9025g1

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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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