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	15600h	Isogeny class
Conductor	15600	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	38400	Modular degree for the optimal curve
Δ	32432663250000 = 24 · 310 · 56 · 133	Discriminant
Eigenvalues	2+ 3+ 5+  0  2 13- -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-16283,-745938]	[a1,a2,a3,a4,a6]
j	1909913257984/129730653	j-invariant
L	1.2733165338035	L(r)(E,1)/r!
Ω	0.42443884460118	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7800i1 62400gd1 46800bb1 624e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15600h1

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

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Quadratic twists for elliptic curve 15600h1

-4	8	-3	5
7800i1	62400gd1	46800bb1	624e1

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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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