Cremona's table of elliptic curves

316 = 2² · 79

Field	Data	Notes
Atkin-Lehner	2- 79-	Signs for the Atkin-Lehner involutions
Class	316b	Isogeny class
Conductor	316	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	36	Modular degree for the optimal curve
Δ	20224 = 28 · 79	Discriminant
Eigenvalues	2- -3  1  1 -6 -1 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7,-2]	[a1,a2,a3,a4,a6]
Generators	[-1:2:1]	Generators of the group modulo torsion
j	148176/79	j-invariant
L	1.2203951479808	L(r)(E,1)/r!
Ω	3.1195572511036	Real period
R	0.1304026020091	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	1264c1 5056j1 2844e1 7900c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 316b1

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
-	-3	1	1	-6	-1	-4	-6	2	-8	4	4	-6	4	-3	14	-9	6	-10	5	6	-	4	1	-11

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Quadratic twists for elliptic curve 316b1

-4	8	-3	5	-7	-11	13	17	-19	-79
1264c1	5056j1	2844e1	7900c1	15484b1	38236d1	53404i1	91324b1	114076f1	24964d1

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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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