Cremona's table of elliptic curves

3850 = 2 · 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	3850s	Isogeny class
Conductor	3850	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	140118945312500 = 22 · 511 · 72 · 114	Discriminant
Eigenvalues	2-  0 5+ 7- 11+ -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-81666730,-284043362603]	[a1,a2,a3,a4,a6]
Generators	[3355095:1177801411:27]	Generators of the group modulo torsion
j	3855131356812007128171561/8967612500	j-invariant
L	5.081988529	L(r)(E,1)/r!
Ω	0.050221336201935	Real period
R	12.648977788459	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	30800bk4 123200cd4 34650bl4 770c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3850s3

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

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Quadratic twists for elliptic curve 3850s3

-4	8	-3	5	-7	-11
30800bk4	123200cd4	34650bl4	770c3	26950cc4	42350f4

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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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