Cremona's table of elliptic curves

100800 = 2⁶ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	100800fx	Isogeny class
Conductor	100800	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	276480	Modular degree for the optimal curve
Δ	-51030000000000 = -1 · 210 · 36 · 510 · 7	Discriminant
Eigenvalues	2+ 3- 5+ 7-  5  0 -8  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7500,-425000]	[a1,a2,a3,a4,a6]
Generators	[9066556811:3739818807:84604519]	Generators of the group modulo torsion
j	-6400/7	j-invariant
L	7.9538982618403	L(r)(E,1)/r!
Ω	0.24593289217599	Real period
R	16.170871232346	Regulator
r	1	Rank of the group of rational points
S	0.99999999993557	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	100800mo1 12600cg1 11200x1 100800hd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800fx1

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
+	-	+	-	5	0	-8	2	7	-3	4	1	2	-3	-6	10	-4	6	-13	-5	6	-13	16	0	-12

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Quadratic twists for elliptic curve 100800fx1

-4	8	-3	5
100800mo1	12600cg1	11200x1	100800hd1

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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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