Cremona's table of elliptic curves

238 = 2 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 7+ 17+	Signs for the Atkin-Lehner involutions
Class	238d	Isogeny class
Conductor	238	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	3332 = 22 · 72 · 17	Discriminant
Eigenvalues	2-  2  0 7+ -2 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-18,-37]	[a1,a2,a3,a4,a6]
j	647214625/3332	j-invariant
L	2.3178772183314	L(r)(E,1)/r!
Ω	2.3178772183314	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	1904e1 7616b1 2142e1 5950f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 238d1

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

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Quadratic twists for elliptic curve 238d1

-4	8	-3	5	-7	-11	13	17	-19	-23
1904e1	7616b1	2142e1	5950f1	1666n1	28798m1	40222j1	4046q1	85918c1	125902s1

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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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