Cremona's table of elliptic curves

8385 = 3 · 5 · 13 · 43

Field	Data	Notes
Atkin-Lehner	3+ 5+ 13- 43-	Signs for the Atkin-Lehner involutions
Class	8385c	Isogeny class
Conductor	8385	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	116045124609375 = 312 · 58 · 13 · 43	Discriminant
Eigenvalues	1 3+ 5+ -4 -4 13- -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-12473,132258]	[a1,a2,a3,a4,a6]
Generators	[34674:310163:216]	Generators of the group modulo torsion
j	214630225740574489/116045124609375	j-invariant
L	2.9261965642657	L(r)(E,1)/r!
Ω	0.51575398617306	Real period
R	5.6736285956378	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25155o3 41925i3 109005h3	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 8385c3

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	-4	-	-6	8	4	10	8	-6	-2	-	0	-2	4	-2	-4	0	-10	0	4	6	2

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Quadratic twists for elliptic curve 8385c3

-3	5	13
25155o3	41925i3	109005h3

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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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