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	7777d	Isogeny class
Conductor	7777	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	19200	Modular degree for the optimal curve
Δ	173972399909 = 76 · 114 · 101	Discriminant
Eigenvalues	-2 -2 -3 7- 11- -5 -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-2282,-37620]	[a1,a2,a3,a4,a6]
Generators	[-32:60:1] [-21:38:1]	Generators of the group modulo torsion
j	1314803742404608/173972399909	j-invariant
L	1.9611071757769	L(r)(E,1)/r!
Ω	0.69676182536768	Real period
R	0.11727508025803	Regulator
r	2	Rank of the group of rational points
S	0.99999999999978	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	124432g1 69993i1 54439e1 85547b1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7777d1

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	-2	-3	-	-	-5	-3	5	-3	-8	-7	-6	0	-8	9	12	-14	14	-8	-3	-14	-13	6	-4	-2

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Quadratic twists for elliptic curve 7777d1

-4	-3	-7	-11
124432g1	69993i1	54439e1	85547b1

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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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