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	24	Product of Tamagawa factors cp
Δ	-7722894400 = -1 · 26 · 52 · 136	Discriminant
Eigenvalues	2+ -2 5- -4 -6 13- -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,112,-4194]	[a1,a2,a3,a4,a6]
Generators	[17:43:1]	Generators of the group modulo torsion
j	157376536199/7722894400	j-invariant
L	0.73821739879204	L(r)(E,1)/r!
Ω	0.63070483322777	Real period
R	0.19507735893245	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	1040g4 4160b4 1170l4 650j4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 130a4

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 130a4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1040g4	4160b4	1170l4	650j4	6370c4	15730y4	1690f4	37570b4	46930bh4	68770d4	109330ba4	124930e4

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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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