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	4278d	Isogeny class
Conductor	4278	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	268800	Modular degree for the optimal curve
Δ	-8246447729625120768 = -1 · 214 · 316 · 233 · 312	Discriminant
Eigenvalues	2+ 3+ -4 -4  6 -6 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-36342,-138203820]	[a1,a2,a3,a4,a6]
Generators	[3740:226290:1]	Generators of the group modulo torsion
j	-5308463753738358121/8246447729625120768	j-invariant
L	1.3139509202967	L(r)(E,1)/r!
Ω	0.10532599702497	Real period
R	2.0791810781295	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	34224be1 12834p1 106950cf1 98394q1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 4278d1

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	6	-6	-2	-2	-	-2	-	8	6	6	-8	-8	-12	12	6	16	14	-4	2	-6	14

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Quadratic twists for elliptic curve 4278d1

-4	-3	5	-23
34224be1	12834p1	106950cf1	98394q1

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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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