Cremona's table of elliptic curves

77 = 7 · 11

Field	Data	Notes
Atkin-Lehner	7+ 11+	Signs for the Atkin-Lehner involutions
Class	77a	Isogeny class
Conductor	77	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4	Modular degree for the optimal curve
Δ	-539 = -1 · 72 · 11	Discriminant
Eigenvalues	0 -3 -1 7+ 11+ -4  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,2,0]	[a1,a2,a3,a4,a6]
Generators	[2:3:1]	Generators of the group modulo torsion
j	884736/539	j-invariant
L	0.62733620193051	L(r)(E,1)/r!
Ω	3.1997813615949	Real period
R	0.098027979264468	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	1232l1 4928j1 693b1 1925d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 77a1

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	-1	+	+	-4	2	-6	-5	10	1	-5	-2	-8	8	-6	3	-2	-3	1	10	6	12	-15	-5

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Quadratic twists for elliptic curve 77a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
1232l1	4928j1	693b1	1925d1	539b1	847b1	13013r1	22253i1	27797a1	40733k1	64757d1	73997d1	105413a1	129437e1

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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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