Cremona's table of elliptic curves

61800 = 2³ · 3 · 5² · 103

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 103+	Signs for the Atkin-Lehner involutions
Class	61800m	Isogeny class
Conductor	61800	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	59904	Modular degree for the optimal curve
Δ	-222480000000 = -1 · 210 · 33 · 57 · 103	Discriminant
Eigenvalues	2- 3- 5+ -3  0  4  5 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1008,25488]	[a1,a2,a3,a4,a6]
Generators	[48:300:1]	Generators of the group modulo torsion
j	-7086244/13905	j-invariant
L	7.7648663098817	L(r)(E,1)/r!
Ω	0.88681326068312	Real period
R	0.36483001617536	Regulator
r	1	Rank of the group of rational points
S	1.0000000000171	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	123600f1 12360b1	Quadratic twists by: -4 5

Hecke Eigenvalues for elliptic curve 61800m1

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
-	-	+	-3	0	4	5	-2	6	6	1	3	8	-6	-3	-12	0	-13	-12	-12	-9	-10	2	1	-10

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Quadratic twists for elliptic curve 61800m1

-4	5
123600f1	12360b1

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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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