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	414b	Isogeny class
Conductor	414	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2313846 = 2 · 37 · 232	Discriminant
Eigenvalues	2- 3-  2 -2  6 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-284,-1767]	[a1,a2,a3,a4,a6]
j	3463512697/3174	j-invariant
L	2.326716093051	L(r)(E,1)/r!
Ω	1.1633580465255	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3312o2 13248v2 138a2 10350j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 414b2

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

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Quadratic twists for elliptic curve 414b2

-4	8	-3	5	-7	-11	13	17	-23
3312o2	13248v2	138a2	10350j2	20286cs2	50094bc2	69966r2	119646cd2	9522k2

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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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