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	10450i	Isogeny class
Conductor	10450	Conductor
∏ cp	21	Product of Tamagawa factors cp
deg	35280	Modular degree for the optimal curve
Δ	-106930004711200 = -1 · 25 · 52 · 117 · 193	Discriminant
Eigenvalues	2+ -2 5+  3 11-  0 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,10314,292328]	[a1,a2,a3,a4,a6]
Generators	[536:12376:1]	Generators of the group modulo torsion
j	4854288821119295/4277200188448	j-invariant
L	2.5436484214669	L(r)(E,1)/r!
Ω	0.38733717136823	Real period
R	0.31271492710107	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	83600bh1 94050da1 10450bf1 114950cm1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 10450i1

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 10450i1

-4	-3	5	-11
83600bh1	94050da1	10450bf1	114950cm1

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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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