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	130b	Isogeny class
Conductor	130	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	16640 = 28 · 5 · 13	Discriminant
Eigenvalues	2-  0 5-  0  0 13-  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-7,-1]	[a1,a2,a3,a4,a6]
j	33076161/16640	j-invariant
L	1.564713754401	L(r)(E,1)/r!
Ω	3.1294275088021	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1040f1 4160a1 1170c1 650a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 130b1

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
-	0	-	0	0	-	2	-8	-4	-2	-4	6	10	0	8	6	8	-2	4	-12	10	-8	12	10	-14

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Quadratic twists for elliptic curve 130b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1040f1	4160a1	1170c1	650a1	6370l1	15730k1	1690a1	37570j1	46930r1	68770p1	109330l1	124930j1

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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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