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	61200cc	Isogeny class
Conductor	61200	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-17535400992000000 = -1 · 211 · 38 · 56 · 174	Discriminant
Eigenvalues	2+ 3- 5+ -4  4 -6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,64725,648250]	[a1,a2,a3,a4,a6]
Generators	[41:1836:1]	Generators of the group modulo torsion
j	1285471294/751689	j-invariant
L	4.8691392869487	L(r)(E,1)/r!
Ω	0.23543885333241	Real period
R	0.64628501439023	Regulator
r	1	Rank of the group of rational points
S	1.000000000021	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30600co3 20400z4 2448d4	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 61200cc3

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	4	-6	-	-4	4	6	4	-10	6	4	8	6	-4	-14	-12	-12	-10	4	-4	6	6

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Quadratic twists for elliptic curve 61200cc3

-4	-3	5
30600co3	20400z4	2448d4

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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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