Cremona's table of elliptic curves

304 = 2⁴ · 19

Field	Data	Notes
Atkin-Lehner	2- 19-	Signs for the Atkin-Lehner involutions
Class	304f	Isogeny class
Conductor	304	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-4864 = -1 · 28 · 19	Discriminant
Eigenvalues	2- -2 -1  3 -5 -4 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-21,31]	[a1,a2,a3,a4,a6]
Generators	[3:2:1]	Generators of the group modulo torsion
j	-4194304/19	j-invariant
L	1.2842245405938	L(r)(E,1)/r!
Ω	4.3504123451183	Real period
R	0.14759802505099	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	76a1 1216k1 2736r1 7600r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 304f1

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	-1	3	-5	-4	-3	-	-8	-2	-4	10	10	-1	1	-4	-6	-13	12	-2	9	-8	12	12	-8

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Quadratic twists for elliptic curve 304f1

-4	8	-3	5	-7	-11	13	17	-19
76a1	1216k1	2736r1	7600r1	14896ba1	36784w1	51376p1	87856r1	5776p1

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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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