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	1050i	Isogeny class
Conductor	1050	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	-1446700500 = -1 · 22 · 310 · 53 · 72	Discriminant
Eigenvalues	2+ 3- 5- 7+ -2 -2 -8 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-71,1838]	[a1,a2,a3,a4,a6]
Generators	[33:-206:1]	Generators of the group modulo torsion
j	-310288733/11573604	j-invariant
L	2.1273386355558	L(r)(E,1)/r!
Ω	1.2605783610187	Real period
R	0.084379468240141	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	8400bt2 33600bf2 3150bo2 1050m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1050i2

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

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Quadratic twists for elliptic curve 1050i2

-4	8	-3	5	-7	-11
8400bt2	33600bf2	3150bo2	1050m2	7350q2	127050jg2

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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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