Cremona's table of elliptic curves

4278 = 2 · 3 · 23 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3- 23- 31+	Signs for the Atkin-Lehner involutions
Class	4278h	Isogeny class
Conductor	4278	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	61440	Modular degree for the optimal curve
Δ	-2659576801689796608 = -1 · 216 · 38 · 235 · 312	Discriminant
Eigenvalues	2+ 3- -2 -2  0 -2  4  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-80182,78941384]	[a1,a2,a3,a4,a6]
Generators	[277:8693:1]	Generators of the group modulo torsion
j	-57009414456430203097/2659576801689796608	j-invariant
L	2.7034384028723	L(r)(E,1)/r!
Ω	0.21238127405791	Real period
R	0.31822937484299	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	34224w1 12834k1 106950bj1 98394t1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 4278h1

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	-2	0	-2	4	2	-	2	+	4	-2	0	4	-4	0	-4	2	-12	14	-16	12	4	-18

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Quadratic twists for elliptic curve 4278h1

-4	-3	5	-23
34224w1	12834k1	106950bj1	98394t1

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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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