Cremona's table of elliptic curves

150 = 2 · 3 · 5²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+	Signs for the Atkin-Lehner involutions
Class	150c	Isogeny class
Conductor	150	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-24000000000 = -1 · 212 · 3 · 59	Discriminant
Eigenvalues	2- 3+ 5+  4  0 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-338,-7969]	[a1,a2,a3,a4,a6]
j	-273359449/1536000	j-invariant
L	1.4990368329452	L(r)(E,1)/r!
Ω	0.49967894431507	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1200p3 4800w3 450g3 30a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 150c3

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	-2	-6	-4	0	-6	8	-2	-6	4	0	6	0	-10	4	0	-2	8	-12	18	-2

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Quadratic twists for elliptic curve 150c3

-4	8	-3	5	-7	-11	13	17	-19	-23	29
1200p3	4800w3	450g3	30a3	7350cj3	18150m3	25350i3	43350dd3	54150bb3	79350cr3	126150bc3

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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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