Cremona's table of elliptic curves

18200 = 2³ · 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 13+	Signs for the Atkin-Lehner involutions
Class	18200ba	Isogeny class
Conductor	18200	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	5632	Modular degree for the optimal curve
Δ	20384000 = 28 · 53 · 72 · 13	Discriminant
Eigenvalues	2- -2 5- 7- -6 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-68,-32]	[a1,a2,a3,a4,a6]
Generators	[-8:8:1] [-6:14:1]	Generators of the group modulo torsion
j	1102736/637	j-invariant
L	5.265179653123	L(r)(E,1)/r!
Ω	1.8139317519964	Real period
R	0.72565845535929	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	36400t1 18200i1 127400cg1	Quadratic twists by: -4 5 -7

Hecke Eigenvalues for elliptic curve 18200ba1

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

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Quadratic twists for elliptic curve 18200ba1

-4	5	-7
36400t1	18200i1	127400cg1

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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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