Cremona's table of elliptic curves

938 = 2 · 7 · 67

Field	Data	Notes
Atkin-Lehner	2+ 7- 67-	Signs for the Atkin-Lehner involutions
Class	938a	Isogeny class
Conductor	938	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	1876 = 22 · 7 · 67	Discriminant
Eigenvalues	2+  1 -1 7-  2 -7 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4,-2]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1]	Generators of the group modulo torsion
j	4826809/1876	j-invariant
L	2.0114613918831	L(r)(E,1)/r!
Ω	3.6024689922791	Real period
R	0.27917816866628	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7504n1 30016p1 8442d1 23450k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 938a1

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
+	1	-1	-	2	-7	-2	-2	1	-5	9	-9	3	-6	12	-10	-8	-2	-	9	-2	-8	2	2	-18

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Quadratic twists for elliptic curve 938a1

-4	8	-3	5	-7	-11	-67
7504n1	30016p1	8442d1	23450k1	6566e1	113498o1	62846f1

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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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