Cremona's table of elliptic curves

108300 = 2² · 3 · 5² · 19²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 19+	Signs for the Atkin-Lehner involutions
Class	108300ba	Isogeny class
Conductor	108300	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	432000	Modular degree for the optimal curve
Δ	-166673700000000 = -1 · 28 · 35 · 58 · 193	Discriminant
Eigenvalues	2- 3+ 5-  2 -3  4  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-84708,9537912]	[a1,a2,a3,a4,a6]
Generators	[317:3800:1]	Generators of the group modulo torsion
j	-98003440/243	j-invariant
L	6.779299867999	L(r)(E,1)/r!
Ω	0.57487856974449	Real period
R	1.9654295216466	Regulator
r	1	Rank of the group of rational points
S	0.99999999911085	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	108300br1 108300co1	Quadratic twists by: 5 -19

Hecke Eigenvalues for elliptic curve 108300ba1

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	-3	4	6	+	3	1	-3	-4	2	-4	-8	5	12	-7	-13	6	15	-1	5	5	-6

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Quadratic twists for elliptic curve 108300ba1

5	-19
108300br1	108300co1

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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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