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	238a	Isogeny class
Conductor	238	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	13647872 = 214 · 72 · 17	Discriminant
Eigenvalues	2- -2 -4 7- -6 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-60,16]	[a1,a2,a3,a4,a6]
Generators	[-4:16:1]	Generators of the group modulo torsion
j	23912763841/13647872	j-invariant
L	1.4310007528473	L(r)(E,1)/r!
Ω	1.9151889278601	Real period
R	0.1067407376914	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	1904a1 7616c1 2142k1 5950b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 238a1

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	-4	-	-6	-2	+	0	-4	8	0	4	-2	-8	-8	-6	-4	-8	-16	4	10	-12	12	10	6

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Quadratic twists for elliptic curve 238a1

-4	8	-3	5	-7	-11	13	17	-19	-23
1904a1	7616c1	2142k1	5950b1	1666m1	28798e1	40222d1	4046l1	85918k1	125902p1

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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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