Cremona's table of elliptic curves

605 = 5 · 11²

Field	Data	Notes
Atkin-Lehner	5- 11-	Signs for the Atkin-Lehner involutions
Class	605b	Isogeny class
Conductor	605	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	12179481875 = 54 · 117	Discriminant
Eigenvalues	-1  0 5-  0 11- -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-7162,-231426]	[a1,a2,a3,a4,a6]
Generators	[-48:26:1]	Generators of the group modulo torsion
j	22930509321/6875	j-invariant
L	1.463218542434	L(r)(E,1)/r!
Ω	0.51898347191497	Real period
R	1.4096966682147	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	9680w4 38720c4 5445e4 3025b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 605b3

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	-	-2	-6	4	4	-6	-8	-2	-2	-4	-12	-2	4	10	-16	8	-14	-8	4	10	10

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Quadratic twists for elliptic curve 605b3

-4	8	-3	5	-7	-11	13
9680w4	38720c4	5445e4	3025b3	29645h4	55a3	102245b4

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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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