Cremona's table of elliptic curves

15600 = 2⁴ · 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	15600r	Isogeny class
Conductor	15600	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	749554884000000000 = 211 · 38 · 59 · 134	Discriminant
Eigenvalues	2+ 3- 5+  0  0 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-247408,22467188]	[a1,a2,a3,a4,a6]
Generators	[-532:1950:1]	Generators of the group modulo torsion
j	52337949619538/23423590125	j-invariant
L	6.0422206991205	L(r)(E,1)/r!
Ω	0.25550018199376	Real period
R	1.478037278675	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	7800o3 62400dx4 46800ba4 3120a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15600r3

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

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Quadratic twists for elliptic curve 15600r3

-4	8	-3	5
7800o3	62400dx4	46800ba4	3120a3

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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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