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	13300h	Isogeny class
Conductor	13300	Conductor
∏ cp	18	Product of Tamagawa factors cp
Δ	-6454694873200 = -1 · 24 · 52 · 73 · 196	Discriminant
Eigenvalues	2-  2 5+ 7+  3 -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4758,177377]	[a1,a2,a3,a4,a6]
Generators	[116:1083:1]	Generators of the group modulo torsion
j	-29787105760000/16136737183	j-invariant
L	6.4802053263672	L(r)(E,1)/r!
Ω	0.69866743671428	Real period
R	0.51528293448664	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	53200cn2 119700u2 13300y2 93100m2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13300h2

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	+	+	3	-2	-6	-	3	-9	2	1	0	1	12	6	-12	8	1	9	4	-13	0	-12	10

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Quadratic twists for elliptic curve 13300h2

-4	-3	5	-7
53200cn2	119700u2	13300y2	93100m2

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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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