Cremona's table of elliptic curves

13300 = 2² · 5² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 19-	Signs for the Atkin-Lehner involutions
Class	13300r	Isogeny class
Conductor	13300	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	631680	Modular degree for the optimal curve
Δ	-5.36624736515E+19	Discriminant
Eigenvalues	2-  1 5- 7+ -5  3 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-29742333,62423572463]	[a1,a2,a3,a4,a6]
j	-5819408145941159936/107324947303	j-invariant
L	1.4658705759198	L(r)(E,1)/r!
Ω	0.18323382198998	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	53200ds1 119700ca1 13300w1 93100bm1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13300r1

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	-	+	-5	3	-3	-	2	3	-2	-6	-6	0	-11	2	10	4	2	16	-6	-3	12	-4	9

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Quadratic twists for elliptic curve 13300r1

-4	-3	5	-7
53200ds1	119700ca1	13300w1	93100bm1

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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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