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	16	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-195570288 = -1 · 24 · 312 · 23	Discriminant
Eigenvalues	2- 3-  0  2  0  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-320,-2221]	[a1,a2,a3,a4,a6]
j	-4956477625/268272	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	2	Number of elements in the torsion subgroup
Twists	3312n1 13248o1 138b1 10350l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 414a1

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 414a1

-4	8	-3	5	-7	-11	13	17	-23
3312n1	13248o1	138b1	10350l1	20286cm1	50094y1	69966n1	119646br1	9522h1

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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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