Cremona's table of elliptic curves

6900 = 2² · 3 · 5² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 23-	Signs for the Atkin-Lehner involutions
Class	6900i	Isogeny class
Conductor	6900	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	7200	Modular degree for the optimal curve
Δ	217300320000 = 28 · 310 · 54 · 23	Discriminant
Eigenvalues	2- 3- 5-  3 -5  1 -4 -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3708,-85212]	[a1,a2,a3,a4,a6]
Generators	[-36:54:1]	Generators of the group modulo torsion
j	35248450000/1358127	j-invariant
L	5.1240386124813	L(r)(E,1)/r!
Ω	0.61324539345042	Real period
R	0.27852029368162	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27600by1 110400co1 20700s1 6900b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6900i1

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	-5	1	-4	-3	-	-3	0	2	-7	-3	-4	4	-12	-6	12	0	-3	-5	-1	0	-10

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Quadratic twists for elliptic curve 6900i1

-4	8	-3	5
27600by1	110400co1	20700s1	6900b1

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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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