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	20	Product of Tamagawa factors cp
Δ	-20284203008 = -1 · 213 · 195	Discriminant
Eigenvalues	2-  1 -4 -3 -2 -1  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1120,15604]	[a1,a2,a3,a4,a6]
Generators	[-30:152:1]	Generators of the group modulo torsion
j	-37966934881/4952198	j-invariant
L	1.5451623820953	L(r)(E,1)/r!
Ω	1.1779812106888	Real period
R	0.065585187950147	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	38b2 1216j2 2736x2 7600p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 304a2

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 304a2

-4	8	-3	5	-7	-11	13	17	-19
38b2	1216j2	2736x2	7600p2	14896z2	36784u2	51376o2	87856q2	5776o2

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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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