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	238b	Isogeny class
Conductor	238	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-476 = -1 · 22 · 7 · 17	Discriminant
Eigenvalues	2+  0 -2 7+ -2  0 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,2,0]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	658503/476	j-invariant
L	1.072323770296	L(r)(E,1)/r!
Ω	3.340744690228	Real period
R	0.64196690841574	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	1904d1 7616a1 2142p1 5950p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 238b1

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	-2	+	-2	0	+	-2	-8	0	8	-4	-6	4	8	-6	10	10	8	4	-10	-4	-6	-6	-14

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Quadratic twists for elliptic curve 238b1

-4	8	-3	5	-7	-11	13	17	-19	-23
1904d1	7616a1	2142p1	5950p1	1666d1	28798ba1	40222u1	4046e1	85918bc1	125902g1

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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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