Cremona's table of elliptic curves

414 = 2 · 3² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 23-	Signs for the Atkin-Lehner involutions
Class	414a	Isogeny class
Conductor	414	Conductor
∏ cp	144	Product of Tamagawa factors cp
Δ	-326974205952 = -1 · 212 · 38 · 233	Discriminant
Eigenvalues	2- 3-  0  2  0  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,1705,-5137]	[a1,a2,a3,a4,a6]
j	752329532375/448524288	j-invariant
L	2.2510426674949	L(r)(E,1)/r!
Ω	0.56276066687373	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	3312n3 13248o3 138b3 10350l3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 414a3

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

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Quadratic twists for elliptic curve 414a3

-4	8	-3	5	-7	-11	13	17	-23
3312n3	13248o3	138b3	10350l3	20286cm3	50094y3	69966n3	119646br3	9522h3

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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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