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	1300d	Isogeny class
Conductor	1300	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	211250000 = 24 · 57 · 132	Discriminant
Eigenvalues	2- -2 5+ -2  4 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7033,224688]	[a1,a2,a3,a4,a6]
Generators	[73:-325:1]	Generators of the group modulo torsion
j	153910165504/845	j-invariant
L	1.9409296438454	L(r)(E,1)/r!
Ω	1.5781444770912	Real period
R	0.40996027761726	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5200z1 20800m1 11700r1 260a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1300d1

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	+	-2	4	-	-2	0	6	-10	0	-10	-2	-2	6	-2	-8	2	6	-8	-10	-16	-6	10	-2

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Quadratic twists for elliptic curve 1300d1

-4	8	-3	5	-7	13
5200z1	20800m1	11700r1	260a1	63700n1	16900m1

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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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