Cremona's table of elliptic curves

2278 = 2 · 17 · 67

Field	Data	Notes
Atkin-Lehner	2+ 17+ 67-	Signs for the Atkin-Lehner involutions
Class	2278a	Isogeny class
Conductor	2278	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1232	Modular degree for the optimal curve
Δ	1250312192 = 214 · 17 · 672	Discriminant
Eigenvalues	2+  0  0  2  4  6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1547,23749]	[a1,a2,a3,a4,a6]
j	409593028559625/1250312192	j-invariant
L	1.538591520939	L(r)(E,1)/r!
Ω	1.538591520939	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	18224f1 72896a1 20502bd1 56950n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2278a1

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

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Quadratic twists for elliptic curve 2278a1

-4	8	-3	5	-7	17
18224f1	72896a1	20502bd1	56950n1	111622g1	38726a1

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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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