Cremona's table of elliptic curves

195 = 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	3- 5- 13-	Signs for the Atkin-Lehner involutions
Class	195a	Isogeny class
Conductor	195	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	594140625 = 32 · 58 · 132	Discriminant
Eigenvalues	-1 3- 5-  0  4 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-8125,-282568]	[a1,a2,a3,a4,a6]
j	59319456301170001/594140625	j-invariant
L	1.0057121353225	L(r)(E,1)/r!
Ω	0.50285606766124	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3120r5 12480a5 585f5 975a5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 195a5

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	4	-	2	-4	8	-2	-8	6	-6	-4	-8	6	-12	-2	-4	0	-6	16	-4	10	18

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Quadratic twists for elliptic curve 195a5

-4	8	-3	5	-7	-11	13	17	-19	-23
3120r5	12480a5	585f5	975a5	9555e5	23595n6	2535f5	56355b6	70395g6	103155h6

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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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