Cremona's table of elliptic curves

7777 = 7 · 11 · 101

Field	Data	Notes
Atkin-Lehner	7+ 11+ 101-	Signs for the Atkin-Lehner involutions
Class	7777a	Isogeny class
Conductor	7777	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	299324076821 = 74 · 112 · 1013	Discriminant
Eigenvalues	0  0 -1 7+ 11+ -1 -7 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-2588,43302]	[a1,a2,a3,a4,a6]
Generators	[-12:269:1] [18:50:1]	Generators of the group modulo torsion
j	1916975348711424/299324076821	j-invariant
L	4.4199504103678	L(r)(E,1)/r!
Ω	0.9295665193814	Real period
R	0.39623759374337	Regulator
r	2	Rank of the group of rational points
S	0.99999999999972	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	124432r1 69993f1 54439a1 85547e1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7777a1

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	0	-1	+	+	-1	-7	-3	1	-8	7	-2	-2	-8	-1	-12	-6	-2	-12	-11	-8	-3	0	0	-2

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Quadratic twists for elliptic curve 7777a1

-4	-3	-7	-11
124432r1	69993f1	54439a1	85547e1

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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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