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	414d	Isogeny class
Conductor	414	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	12340512 = 25 · 36 · 232	Discriminant
Eigenvalues	2- 3- -4 -4 -2 -2  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1532,23455]	[a1,a2,a3,a4,a6]
Generators	[17:37:1]	Generators of the group modulo torsion
j	545138290809/16928	j-invariant
L	2.0793639153686	L(r)(E,1)/r!
Ω	2.0997210459507	Real period
R	0.19806096808703	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	3312r2 13248l2 46a2 10350s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 414d2

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

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Quadratic twists for elliptic curve 414d2

-4	8	-3	5	-7	-11	13	17	-23
3312r2	13248l2	46a2	10350s2	20286ck2	50094x2	69966l2	119646cr2	9522p2

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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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