Cremona's table of elliptic curves

399 = 3 · 7 · 19

Field	Data	Notes
Atkin-Lehner	3+ 7- 19-	Signs for the Atkin-Lehner involutions
Class	399b	Isogeny class
Conductor	399	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	25137 = 33 · 72 · 19	Discriminant
Eigenvalues	-1 3+  0 7- -2  0 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-13,-22]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1]	Generators of the group modulo torsion
j	244140625/25137	j-invariant
L	1.1285450387598	L(r)(E,1)/r!
Ω	2.5299798485191	Real period
R	0.89213757130942	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6384bb1 25536bm1 1197e1 9975k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 399b1

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

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Quadratic twists for elliptic curve 399b1

-4	8	-3	5	-7	-11	13	17	-19
6384bb1	25536bm1	1197e1	9975k1	2793i1	48279d1	67431a1	115311o1	7581f1

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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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