Cremona's table of elliptic curves

850 = 2 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2+ 5- 17-	Signs for the Atkin-Lehner involutions
Class	850d	Isogeny class
Conductor	850	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	6720	Modular degree for the optimal curve
Δ	-2564616706250000 = -1 · 24 · 58 · 177	Discriminant
Eigenvalues	2+  1 5- -5  4  3 17- -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,33924,-387702]	[a1,a2,a3,a4,a6]
Generators	[21:567:1]	Generators of the group modulo torsion
j	11053587253415/6565418768	j-invariant
L	1.8987366857377	L(r)(E,1)/r!
Ω	0.26693834391184	Real period
R	0.5080725645996	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6800y1 27200bm1 7650cm1 850f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 850d1

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
+	1	-	-5	4	3	-	-2	-8	0	-5	-12	-10	-4	-2	-1	0	2	8	5	4	-17	-16	-6	16

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Quadratic twists for elliptic curve 850d1

-4	8	-3	5	-7	-11	17
6800y1	27200bm1	7650cm1	850f1	41650x1	102850da1	14450m1

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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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