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	8385a	Isogeny class
Conductor	8385	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	22177512703125 = 310 · 56 · 13 · 432	Discriminant
Eigenvalues	-1 3+ 5+  2  2 13+  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1083551,433680824]	[a1,a2,a3,a4,a6]
Generators	[74:18775:1]	Generators of the group modulo torsion
j	140692779321470594548849/22177512703125	j-invariant
L	2.3792352210995	L(r)(E,1)/r!
Ω	0.5315616468256	Real period
R	2.2379673508312	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	25155l2 41925l2 109005e2	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 8385a2

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

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Quadratic twists for elliptic curve 8385a2

-3	5	13
25155l2	41925l2	109005e2

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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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