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	130c	Isogeny class
Conductor	130	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-26406250000 = -1 · 24 · 510 · 132	Discriminant
Eigenvalues	2-  2 5+ -4 -2 13+  2  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-761,-11561]	[a1,a2,a3,a4,a6]
j	-48743122863889/26406250000	j-invariant
L	1.7730949037663	L(r)(E,1)/r!
Ω	0.44327372594157	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1040e2 4160i2 1170f2 650e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 130c2

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	-2	+	2	6	6	2	-6	-2	10	-10	-12	2	10	2	-12	10	10	-4	0	-14	14

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Quadratic twists for elliptic curve 130c2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1040e2	4160i2	1170f2	650e2	6370bb2	15730i2	1690e2	37570q2	46930l2	68770s2	109330d2	124930g2

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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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