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	7623g	Isogeny class
Conductor	7623	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-38900169 = -1 · 38 · 72 · 112	Discriminant
Eigenvalues	1 3-  3 7+ 11- -7  3  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,27,-302]	[a1,a2,a3,a4,a6]
Generators	[6:4:1]	Generators of the group modulo torsion
j	24167/441	j-invariant
L	5.6665474134379	L(r)(E,1)/r!
Ω	0.99673531672434	Real period
R	1.4212768721942	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	121968gg1 2541c1 53361bl1 7623q1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7623g1

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	-	3	+	-	-7	3	2	4	7	-10	1	-5	-6	6	5	6	-10	-8	10	-10	2	-16	-3	-19

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Quadratic twists for elliptic curve 7623g1

-4	-3	-7	-11
121968gg1	2541c1	53361bl1	7623q1

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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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