Cremona's table of elliptic curves

4114 = 2 · 11² · 17

Field	Data	Notes
Atkin-Lehner	2+ 11- 17-	Signs for the Atkin-Lehner involutions
Class	4114b	Isogeny class
Conductor	4114	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	4095849032 = 23 · 116 · 172	Discriminant
Eigenvalues	2+ -2  0  4 11- -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-5206,-144960]	[a1,a2,a3,a4,a6]
Generators	[-330:175:8]	Generators of the group modulo torsion
j	8805624625/2312	j-invariant
L	2.1417680440097	L(r)(E,1)/r!
Ω	0.56206992810684	Real period
R	3.8105010371637	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	32912bb2 37026ba2 102850ce2 34a2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4114b2

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

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Quadratic twists for elliptic curve 4114b2

-4	-3	5	-11	17
32912bb2	37026ba2	102850ce2	34a2	69938e2

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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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