Cremona's table of elliptic curves

8450 = 2 · 5² · 13²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	8450d	Isogeny class
Conductor	8450	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4320	Modular degree for the optimal curve
Δ	-3861447200 = -1 · 25 · 52 · 136	Discriminant
Eigenvalues	2+ -1 5+  2  3 13+  3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-510,5140]	[a1,a2,a3,a4,a6]
Generators	[-21:95:1]	Generators of the group modulo torsion
j	-121945/32	j-invariant
L	2.7807808784489	L(r)(E,1)/r!
Ω	1.3268584378466	Real period
R	1.047881521921	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	67600br1 76050ek1 8450x3 50b1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8450d1

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	+	2	3	+	3	-5	-6	0	-2	2	3	4	12	-6	0	2	-13	-12	11	-10	-9	-15	2

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Quadratic twists for elliptic curve 8450d1

-4	-3	5	13
67600br1	76050ek1	8450x3	50b1

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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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