Cremona's table of elliptic curves

10478 = 2 · 13² · 31

Field	Data	Notes
Atkin-Lehner	2+ 13- 31-	Signs for the Atkin-Lehner involutions
Class	10478i	Isogeny class
Conductor	10478	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	20736	Modular degree for the optimal curve
Δ	-1038835526144 = -1 · 29 · 133 · 314	Discriminant
Eigenvalues	2+ -1 -1 -5  4 13- -7  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1628,-55856]	[a1,a2,a3,a4,a6]
Generators	[57:173:1]	Generators of the group modulo torsion
j	-217407044197/472842752	j-invariant
L	1.6709376473406	L(r)(E,1)/r!
Ω	0.35195222217809	Real period
R	0.59345329495288	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	83824bf1 94302cn1 10478o1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 10478i1

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	-1	-5	4	-	-7	2	-2	8	-	3	-8	-7	-5	2	6	4	-4	9	14	-10	6	-6	16

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Quadratic twists for elliptic curve 10478i1

-4	-3	13
83824bf1	94302cn1	10478o1

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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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