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	8	Product of Tamagawa factors cp
Δ	3672073602 = 2 · 38 · 234	Discriminant
Eigenvalues	2+ 3- -2  0  0 -2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-963,11371]	[a1,a2,a3,a4,a6]
Generators	[-31:119:1]	Generators of the group modulo torsion
j	135559106353/5037138	j-invariant
L	1.3266055580581	L(r)(E,1)/r!
Ω	1.390561642935	Real period
R	0.47700350602873	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	3312p3 13248r4 138c3 10350bg4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 414c4

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 414c4

-4	8	-3	5	-7	-11	13	17	-23
3312p3	13248r4	138c3	10350bg4	20286bd3	50094cg3	69966bf3	119646p3	9522e3

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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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