Cremona's table of elliptic curves

319 = 11 · 29

Field	Data	Notes
Atkin-Lehner	11+ 29-	Signs for the Atkin-Lehner involutions
Class	319a	Isogeny class
Conductor	319	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	92	Modular degree for the optimal curve
Δ	-9251 = -1 · 11 · 292	Discriminant
Eigenvalues	2 -3  1  4 11+  6  4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-37,-87]	[a1,a2,a3,a4,a6]
j	-5601816576/9251	j-invariant
L	1.9355577615007	L(r)(E,1)/r!
Ω	0.96777888075036	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5104b1 20416c1 2871d1 7975b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 319a1

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	-3	1	4	+	6	4	-2	3	-	-7	-11	4	-4	8	2	-3	2	-15	-7	2	6	-6	9	-17

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Quadratic twists for elliptic curve 319a1

-4	8	-3	5	-7	-11	13	17	-19	29
5104b1	20416c1	2871d1	7975b1	15631d1	3509c1	53911f1	92191b1	115159a1	9251d1

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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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