Cremona's table of elliptic curves

1800 = 2³ · 3² · 5²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5-	Signs for the Atkin-Lehner involutions
Class	1800k	Isogeny class
Conductor	1800	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	1458000 = 24 · 36 · 53	Discriminant
Eigenvalues	2+ 3- 5- -2  4 -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-30,25]	[a1,a2,a3,a4,a6]
Generators	[-4:9:1]	Generators of the group modulo torsion
j	2048	j-invariant
L	2.8509284860122	L(r)(E,1)/r!
Ω	2.3912704446218	Real period
R	0.59611168038818	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	3600s1 14400ch1 200b1 1800w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1800k1

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	4	-4	0	-4	-2	-2	0	-4	-2	6	-6	-4	12	-10	-14	-8	-8	16	2	-6	-16

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Quadratic twists for elliptic curve 1800k1

-4	8	-3	5	-7
3600s1	14400ch1	200b1	1800w1	88200eb1

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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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