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	1300f	Isogeny class
Conductor	1300	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-2080000 = -1 · 28 · 54 · 13	Discriminant
Eigenvalues	2-  0 5- -3  3 13- -1  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,25,-50]	[a1,a2,a3,a4,a6]
j	10800/13	j-invariant
L	1.4020298093217	L(r)(E,1)/r!
Ω	1.4020298093217	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5200bg1 20800bh1 11700z1 1300a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1300f1

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	-	-3	3	-	-1	4	2	7	5	6	4	6	-13	9	5	13	-5	0	-2	-14	-9	4	-2

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Quadratic twists for elliptic curve 1300f1

-4	8	-3	5	-7	13
5200bg1	20800bh1	11700z1	1300a1	63700bi1	16900r1

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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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