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	4	Product of Tamagawa factors cp
Δ	24375 = 3 · 54 · 13	Discriminant
Eigenvalues	-1 3- 5-  0  4 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-130000,-18051943]	[a1,a2,a3,a4,a6]
j	242970740812818720001/24375	j-invariant
L	1.0057121353225	L(r)(E,1)/r!
Ω	0.25142803383062	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3120r7 12480a7 585f7 975a7	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 195a7

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 195a7

-4	8	-3	5	-7	-11	13	17	-19	-23
3120r7	12480a7	585f7	975a7	9555e7	23595n8	2535f7	56355b8	70395g8	103155h8

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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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