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	15600g	Isogeny class
Conductor	15600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-780000000 = -1 · 28 · 3 · 57 · 13	Discriminant
Eigenvalues	2+ 3+ 5+ -5 -1 13+  3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8633,311637]	[a1,a2,a3,a4,a6]
Generators	[52:25:1]	Generators of the group modulo torsion
j	-17790954496/195	j-invariant
L	2.8484955458275	L(r)(E,1)/r!
Ω	1.4448165425717	Real period
R	0.4928818749468	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	7800h1 62400hq1 46800z1 3120l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15600g1

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
+	+	+	-5	-1	+	3	-6	-7	6	2	-1	7	8	2	-13	8	-7	12	-1	10	-3	8	13	-7

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Quadratic twists for elliptic curve 15600g1

-4	8	-3	5
7800h1	62400hq1	46800z1	3120l1

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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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