Cremona's table of elliptic curves

77 = 7 · 11

Field	Data	Notes
Atkin-Lehner	7+ 11-	Signs for the Atkin-Lehner involutions
Class	77c	Isogeny class
Conductor	77	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	6	Modular degree for the optimal curve
Δ	-41503 = -1 · 73 · 112	Discriminant
Eigenvalues	1  2 -2 7+ 11-  4  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,4,11]	[a1,a2,a3,a4,a6]
j	4657463/41503	j-invariant
L	1.3258074292456	L(r)(E,1)/r!
Ω	2.6516148584912	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1232i1 4928e1 693a1 1925f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 77c1

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
1	2	-2	+	-	4	4	0	-4	-6	10	-6	4	12	-10	-6	2	0	8	-12	-8	8	0	-6	-10

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Quadratic twists for elliptic curve 77c1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
1232i1	4928e1	693a1	1925f1	539c1	847c1	13013k1	22253e1	27797b1	40733f1	64757b1	73997b1	105413b1	129437d1

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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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