Cremona's table of elliptic curves

304 = 2⁴ · 19

Field	Data	Notes
Atkin-Lehner	2+ 19+	Signs for the Atkin-Lehner involutions
Class	304c	Isogeny class
Conductor	304	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-38912 = -1 · 211 · 19	Discriminant
Eigenvalues	2+ -1  0 -3 -2  1 -5 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,16]	[a1,a2,a3,a4,a6]
Generators	[0:4:1]	Generators of the group modulo torsion
j	-31250/19	j-invariant
L	1.3932747403697	L(r)(E,1)/r!
Ω	3.3697463258706	Real period
R	0.10336644109329	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	152b1 1216p1 2736e1 7600a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 304c1

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	-3	-2	1	-5	+	1	-3	-4	2	-8	8	8	9	-1	14	-13	-10	9	10	-10	-12	14

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Quadratic twists for elliptic curve 304c1

-4	8	-3	5	-7	-11	13	17	-19
152b1	1216p1	2736e1	7600a1	14896r1	36784i1	51376e1	87856a1	5776c1

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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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