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	1050o	Isogeny class
Conductor	1050	Conductor
∏ cp	125	Product of Tamagawa factors cp
deg	600	Modular degree for the optimal curve
Δ	-3267280800 = -1 · 25 · 35 · 52 · 75	Discriminant
Eigenvalues	2- 3- 5+ 7-  2 -1  3  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,22,-2748]	[a1,a2,a3,a4,a6]
j	46969655/130691232	j-invariant
L	3.2814600886727	L(r)(E,1)/r!
Ω	0.65629201773455	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	8400bh1 33600s1 3150n1 1050d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1050o1

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	-1	3	0	-1	-5	7	-2	7	-11	8	-1	-5	-3	-12	12	-6	10	-11	-10	-2

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Quadratic twists for elliptic curve 1050o1

-4	8	-3	5	-7	-11
8400bh1	33600s1	3150n1	1050d2	7350bt1	127050cp1

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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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