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	13300s	Isogeny class
Conductor	13300	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	35378000 = 24 · 53 · 72 · 192	Discriminant
Eigenvalues	2- -2 5- 7+ -4 -6  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-113,328]	[a1,a2,a3,a4,a6]
Generators	[-11:19:1] [-8:28:1]	Generators of the group modulo torsion
j	80494592/17689	j-invariant
L	4.6715780832876	L(r)(E,1)/r!
Ω	1.9466444329861	Real period
R	0.39996844519798	Regulator
r	2	Rank of the group of rational points
S	0.99999999999979	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53200dt1 119700by1 13300x1 93100bq1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13300s1

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	-	+	-4	-6	0	-	4	-6	-8	-6	-6	0	8	-2	-4	-2	-10	-16	0	0	-12	-14	6

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Quadratic twists for elliptic curve 13300s1

-4	-3	5	-7
53200dt1	119700by1	13300x1	93100bq1

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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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