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	8	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	10400000 = 28 · 55 · 13	Discriminant
Eigenvalues	2-  2 5+ -4 -2 13+  2  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-841,-9737]	[a1,a2,a3,a4,a6]
j	65787589563409/10400000	j-invariant
L	1.7730949037663	L(r)(E,1)/r!
Ω	0.88654745188314	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	1040e1 4160i1 1170f1 650e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 130c1

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 130c1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1040e1	4160i1	1170f1	650e1	6370bb1	15730i1	1690e1	37570q1	46930l1	68770s1	109330d1	124930g1

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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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