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
deg	24	Modular degree for the optimal curve
Δ	26000 = 24 · 53 · 13	Discriminant
Eigenvalues	2+ -2 5- -4 -6 13- -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-33,68]	[a1,a2,a3,a4,a6]
Generators	[-6:10:1]	Generators of the group modulo torsion
j	3803721481/26000	j-invariant
L	0.73821739879204	L(r)(E,1)/r!
Ω	3.7842289993666	Real period
R	1.1704641535947	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	1040g1 4160b1 1170l1 650j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 130a1

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 130a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1040g1	4160b1	1170l1	650j1	6370c1	15730y1	1690f1	37570b1	46930bh1	68770d1	109330ba1	124930e1

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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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