Cremona's table of elliptic curves

10450 = 2 · 5² · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 5- 11- 19-	Signs for the Atkin-Lehner involutions
Class	10450bf	Isogeny class
Conductor	10450	Conductor
∏ cp	105	Product of Tamagawa factors cp
deg	176400	Modular degree for the optimal curve
Δ	-1670781323612500000 = -1 · 25 · 58 · 117 · 193	Discriminant
Eigenvalues	2-  2 5- -3 11-  0  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,257862,36541031]	[a1,a2,a3,a4,a6]
Generators	[381:13603:1]	Generators of the group modulo torsion
j	4854288821119295/4277200188448	j-invariant
L	8.6076757902202	L(r)(E,1)/r!
Ω	0.17322244907837	Real period
R	0.47325196650277	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	83600cm1 94050ca1 10450i1 114950bo1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 10450bf1

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	-	-3	-	0	2	-	-6	-10	0	-3	-7	-2	-2	2	-10	13	2	7	2	-2	0	-18	6

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Quadratic twists for elliptic curve 10450bf1

-4	-3	5	-11
83600cm1	94050ca1	10450i1	114950bo1

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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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