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	150b	Isogeny class
Conductor	150	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	40	Modular degree for the optimal curve
Δ	-23437500 = -1 · 22 · 3 · 59	Discriminant
Eigenvalues	2+ 3+ 5-  2  2  6  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-75,-375]	[a1,a2,a3,a4,a6]
j	-24389/12	j-invariant
L	0.79123678978251	L(r)(E,1)/r!
Ω	0.79123678978251	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1200q1 4800bd1 450a1 150a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 150b1

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

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Quadratic twists for elliptic curve 150b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29
1200q1	4800bd1	450a1	150a1	7350bl1	18150ch1	25350ch1	43350bq1	54150cv1	79350t1	126150de1

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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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