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
deg	64	Modular degree for the optimal curve
Δ	-2414448 = -1 · 24 · 38 · 23	Discriminant
Eigenvalues	2+ 3- -2  0  0 -2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,27,-59]	[a1,a2,a3,a4,a6]
Generators	[5:11:1]	Generators of the group modulo torsion
j	2924207/3312	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	3312p1 13248r1 138c1 10350bg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 414c1

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 414c1

-4	8	-3	5	-7	-11	13	17	-23
3312p1	13248r1	138c1	10350bg1	20286bd1	50094cg1	69966bf1	119646p1	9522e1

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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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