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	-10562500 = -1 · 22 · 56 · 132	Discriminant
Eigenvalues	2+ -2 5- -4 -6 13- -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-13,156]	[a1,a2,a3,a4,a6]
Generators	[-5:12:1]	Generators of the group modulo torsion
j	-217081801/10562500	j-invariant
L	0.73821739879204	L(r)(E,1)/r!
Ω	1.8921144996833	Real period
R	0.58523207679736	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	1040g2 4160b2 1170l2 650j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 130a2

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 130a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1040g2	4160b2	1170l2	650j2	6370c2	15730y2	1690f2	37570b2	46930bh2	68770d2	109330ba2	124930e2

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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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