Cremona's table of elliptic curves

22800 = 2⁴ · 3 · 5² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 19-	Signs for the Atkin-Lehner involutions
Class	22800s	Isogeny class
Conductor	22800	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	684000000000 = 211 · 32 · 59 · 19	Discriminant
Eigenvalues	2+ 3+ 5-  4  0  0 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-101208,-12359088]	[a1,a2,a3,a4,a6]
Generators	[63462:3046274:27]	Generators of the group modulo torsion
j	28662399178/171	j-invariant
L	5.0008569769604	L(r)(E,1)/r!
Ω	0.26766749951235	Real period
R	9.3415468558403	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11400q2 91200iw2 68400cz2 22800bo2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22800s2

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

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Quadratic twists for elliptic curve 22800s2

-4	8	-3	5
11400q2	91200iw2	68400cz2	22800bo2

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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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