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	256	Product of Tamagawa factors cp
deg	61440	Modular degree for the optimal curve
Δ	-792660137500000000 = -1 · 28 · 511 · 78 · 11	Discriminant
Eigenvalues	2-  0 5+ 7- 11+ -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-302230,-76896603]	[a1,a2,a3,a4,a6]
Generators	[1335:42893:1]	Generators of the group modulo torsion
j	-195395722614328041/50730248800000	j-invariant
L	5.081988529	L(r)(E,1)/r!
Ω	0.10044267240387	Real period
R	3.1622444471147	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	30800bk1 123200cd1 34650bl1 770c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3850s1

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 3850s1

-4	8	-3	5	-7	-11
30800bk1	123200cd1	34650bl1	770c1	26950cc1	42350f1

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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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