Cremona's table of elliptic curves

1300 = 2² · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	1300c	Isogeny class
Conductor	1300	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	83200 = 28 · 52 · 13	Discriminant
Eigenvalues	2-  1 5+ -2 -2 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-13,-17]	[a1,a2,a3,a4,a6]
Generators	[-3:2:1]	Generators of the group modulo torsion
j	40960/13	j-invariant
L	2.8817127713753	L(r)(E,1)/r!
Ω	2.5609573371472	Real period
R	0.37508275122685	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5200x1 20800i1 11700q1 1300e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1300c1

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
-	1	+	-2	-2	-	-2	0	3	-7	-6	-4	-8	1	0	1	4	-1	-6	-8	14	5	0	-14	4

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Quadratic twists for elliptic curve 1300c1

-4	8	-3	5	-7	13
5200x1	20800i1	11700q1	1300e1	63700l1	16900c1

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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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