Cremona's table of elliptic curves

1904 = 2⁴ · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 7+ 17+	Signs for the Atkin-Lehner involutions
Class	1904b	Isogeny class
Conductor	1904	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-8485076992 = -1 · 222 · 7 · 172	Discriminant
Eigenvalues	2- -2  4 7+  4 -4 17+  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,504,1012]	[a1,a2,a3,a4,a6]
j	3449795831/2071552	j-invariant
L	1.6010164220934	L(r)(E,1)/r!
Ω	0.80050821104671	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	238e1 7616f1 17136bi1 47600bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1904b1

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	4	+	4	-4	+	6	0	6	-4	-10	6	0	-4	14	6	-12	-4	8	2	0	-10	10	6

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Quadratic twists for elliptic curve 1904b1

-4	8	-3	5	-7	17
238e1	7616f1	17136bi1	47600bb1	13328v1	32368bc1

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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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