Cremona's table of elliptic curves

304 = 2⁴ · 19

Field	Data	Notes
Atkin-Lehner	2- 19-	Signs for the Atkin-Lehner involutions
Class	304a	Isogeny class
Conductor	304	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-2490368 = -1 · 217 · 19	Discriminant
Eigenvalues	2-  1 -4 -3 -2 -1  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,0,-76]	[a1,a2,a3,a4,a6]
Generators	[10:32:1]	Generators of the group modulo torsion
j	-1/608	j-invariant
L	1.5451623820953	L(r)(E,1)/r!
Ω	1.1779812106888	Real period
R	0.32792593975074	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	38b1 1216j1 2736x1 7600p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 304a1

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	-4	-3	-2	-1	3	-	1	-5	8	-2	-8	-4	-8	-1	-15	2	-3	-2	9	10	6	0	-2

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Quadratic twists for elliptic curve 304a1

-4	8	-3	5	-7	-11	13	17	-19
38b1	1216j1	2736x1	7600p1	14896z1	36784u1	51376o1	87856q1	5776o1

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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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