Cremona's table of elliptic curves

7821 = 3² · 11 · 79

Field	Data	Notes
Atkin-Lehner	3- 11- 79+	Signs for the Atkin-Lehner involutions
Class	7821d	Isogeny class
Conductor	7821	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2520	Modular degree for the optimal curve
Δ	-50046579 = -1 · 36 · 11 · 792	Discriminant
Eigenvalues	2 3- -1 -2 11-  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,87,135]	[a1,a2,a3,a4,a6]
Generators	[36:837:64]	Generators of the group modulo torsion
j	99897344/68651	j-invariant
L	7.4245580580794	L(r)(E,1)/r!
Ω	1.2648855340738	Real period
R	2.9348734956939	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	125136p1 869b1 86031k1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 7821d1

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
2	-	-1	-2	-	2	0	2	9	0	-5	5	-12	-8	-4	2	13	-10	9	1	-14	+	-12	9	-7

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Quadratic twists for elliptic curve 7821d1

-4	-3	-11
125136p1	869b1	86031k1

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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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