Cremona's table of elliptic curves

10404 = 2² · 3² · 17²

Field	Data	Notes
Atkin-Lehner	2- 3+ 17-	Signs for the Atkin-Lehner involutions
Class	10404f	Isogeny class
Conductor	10404	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-26303101488 = -1 · 24 · 39 · 174	Discriminant
Eigenvalues	2- 3+  0 -1  0  5 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,0,-7803]	[a1,a2,a3,a4,a6]
Generators	[546:4455:8]	Generators of the group modulo torsion
j	0	j-invariant
L	4.512687265716	L(r)(E,1)/r!
Ω	0.54532421124926	Real period
R	4.1376186611796	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	41616bs2 10404f1 10404a2	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 10404f2

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
-	+	0	-1	0	5	-	-1	0	0	-7	-1	0	5	0	0	0	-1	11	0	-10	-4	0	0	-19

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Quadratic twists for elliptic curve 10404f2

-4	-3	17
41616bs2	10404f1	10404a2

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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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