Cremona's table of elliptic curves

7623 = 3² · 7 · 11²

Field	Data	Notes
Atkin-Lehner	3- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	7623i	Isogeny class
Conductor	7623	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	75047370277958001 = 310 · 72 · 1110	Discriminant
Eigenvalues	-1 3-  2 7+ 11- -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-309299,-64806222]	[a1,a2,a3,a4,a6]
Generators	[13342:502815:8]	Generators of the group modulo torsion
j	2533811507137/58110129	j-invariant
L	2.7504467999361	L(r)(E,1)/r!
Ω	0.20272696036006	Real period
R	6.7836236360745	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	121968fv4 2541b3 53361bp4 693d3	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7623i3

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	-	2	+	-	-6	2	-4	0	-2	8	6	10	4	8	-6	-4	10	-12	0	-2	-16	4	-18	2

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Quadratic twists for elliptic curve 7623i3

-4	-3	-7	-11
121968fv4	2541b3	53361bp4	693d3

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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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