Cremona's table of elliptic curves

1050 = 2 · 3 · 5² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7+	Signs for the Atkin-Lehner involutions
Class	1050a	Isogeny class
Conductor	1050	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	40516875000 = 23 · 33 · 57 · 74	Discriminant
Eigenvalues	2+ 3+ 5+ 7+  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-144025,20978125]	[a1,a2,a3,a4,a6]
Generators	[225:50:1]	Generators of the group modulo torsion
j	21145699168383889/2593080	j-invariant
L	1.6285819080721	L(r)(E,1)/r!
Ω	0.89014505837211	Real period
R	1.829569116578	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	8400ce4 33600cc5 3150bf4 210a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1050a4

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

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Quadratic twists for elliptic curve 1050a4

-4	8	-3	5	-7	-11
8400ce4	33600cc5	3150bf4	210a4	7350w4	127050gb5

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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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