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	7623f	Isogeny class
Conductor	7623	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-202232026977976611 = -1 · 36 · 76 · 119	Discriminant
Eigenvalues	0 3- -3 7+ 11-  4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-53724,22160817]	[a1,a2,a3,a4,a6]
Generators	[-990:41499:8]	Generators of the group modulo torsion
j	-13278380032/156590819	j-invariant
L	2.4108740515359	L(r)(E,1)/r!
Ω	0.2696306335119	Real period
R	2.2353487993321	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	121968gl2 847a2 53361ba2 693c2	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7623f2

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
0	-	-3	+	-	4	-6	-2	-3	-6	5	11	6	-8	0	6	9	10	5	-9	-2	10	12	3	-1

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Quadratic twists for elliptic curve 7623f2

-4	-3	-7	-11
121968gl2	847a2	53361ba2	693c2

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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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