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
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,-19233,-1020257]	[a1,a2,a3,a4,a6]
j	-50357871050752/19	j-invariant
L	1.8243091182881	L(r)(E,1)/r!
Ω	0.20270101314312	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7600m3 30400g3 4275k3 19a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 475a3

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

---

Quadratic twists for elliptic curve 475a3

-4	8	-3	5	-7	-11	13	-19
7600m3	30400g3	4275k3	19a2	23275i3	57475h3	80275a3	9025c3

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations