Cremona's table of elliptic curves

61200 = 2⁴ · 3² · 5² · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 17-	Signs for the Atkin-Lehner involutions
Class	61200du	Isogeny class
Conductor	61200	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	4590000000000000000 = 216 · 33 · 516 · 17	Discriminant
Eigenvalues	2- 3+ 5+ -4  2  6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1662675,-818736750]	[a1,a2,a3,a4,a6]
Generators	[522755:31959326:125]	Generators of the group modulo torsion
j	294172502025843/2656250000	j-invariant
L	5.8679528432237	L(r)(E,1)/r!
Ω	0.1330253342817	Real period
R	11.027885918759	Regulator
r	1	Rank of the group of rational points
S	1.000000000029	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7650e2 61200di2 12240bi2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 61200du2

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

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Quadratic twists for elliptic curve 61200du2

-4	-3	5
7650e2	61200di2	12240bi2

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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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