Cremona's table of elliptic curves

10605 = 3 · 5 · 7 · 101

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7+ 101+	Signs for the Atkin-Lehner involutions
Class	10605a	Isogeny class
Conductor	10605	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1821949605 = -1 · 36 · 5 · 72 · 1012	Discriminant
Eigenvalues	-1 3+ 5+ 7+  0  0  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-371,3278]	[a1,a2,a3,a4,a6]
Generators	[2:49:1]	Generators of the group modulo torsion
j	-5648311006129/1821949605	j-invariant
L	2.0352646807108	L(r)(E,1)/r!
Ω	1.4037100035452	Real period
R	0.72495909966108	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31815m2 53025o2 74235n2	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 10605a2

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	+	+	+	0	0	6	-2	4	-2	2	-2	-2	-12	0	-6	-10	-2	-8	6	-6	12	12	14	8

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Quadratic twists for elliptic curve 10605a2

-3	5	-7
31815m2	53025o2	74235n2

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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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