Cremona's table of elliptic curves

130 = 2 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2+ 5- 13-	Signs for the Atkin-Lehner involutions
Class	130a	Isogeny class
Conductor	130	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	44994560 = 212 · 5 · 133	Discriminant
Eigenvalues	2+ -2 5- -4 -6 13- -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-208,-1122]	[a1,a2,a3,a4,a6]
Generators	[-8:10:1]	Generators of the group modulo torsion
j	988345570681/44994560	j-invariant
L	0.73821739879204	L(r)(E,1)/r!
Ω	1.2614096664555	Real period
R	0.39015471786491	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	1040g3 4160b3 1170l3 650j3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 130a3

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
+	-2	-	-4	-6	-	-6	2	6	-6	2	2	-6	2	-12	6	6	2	-4	-6	-10	-4	0	-6	2

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Quadratic twists for elliptic curve 130a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1040g3	4160b3	1170l3	650j3	6370c3	15730y3	1690f3	37570b3	46930bh3	68770d3	109330ba3	124930e3

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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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