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	2	Product of Tamagawa factors cp
deg	2112	Modular degree for the optimal curve
Δ	477225 = 33 · 52 · 7 · 101	Discriminant
Eigenvalues	-1 3+ 5+ 7+  0  0  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-396,2868]	[a1,a2,a3,a4,a6]
Generators	[6:24:1]	Generators of the group modulo torsion
j	6868751617729/477225	j-invariant
L	2.0352646807108	L(r)(E,1)/r!
Ω	2.8074200070904	Real period
R	1.4499181993222	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	31815m1 53025o1 74235n1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 10605a1

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 10605a1

-3	5	-7
31815m1	53025o1	74235n1

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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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