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	414c	Isogeny class
Conductor	414	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	220016574 = 2 · 314 · 23	Discriminant
Eigenvalues	2+ 3- -2  0  0 -2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2223,-39785]	[a1,a2,a3,a4,a6]
Generators	[-27:16:1]	Generators of the group modulo torsion
j	1666957239793/301806	j-invariant
L	1.3266055580581	L(r)(E,1)/r!
Ω	0.6952808214675	Real period
R	1.9080140241149	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	3312p4 13248r3 138c4 10350bg3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 414c3

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	0	-2	-2	-8	-	2	-8	2	-10	8	-8	-2	4	2	8	0	-6	8	16	-18	10

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Quadratic twists for elliptic curve 414c3

-4	8	-3	5	-7	-11	13	17	-23
3312p4	13248r3	138c4	10350bg3	20286bd4	50094cg4	69966bf4	119646p4	9522e4

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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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