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	938c	Isogeny class
Conductor	938	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	5883136 = 28 · 73 · 67	Discriminant
Eigenvalues	2- -1 -1 7- -4 -3  0  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-56,-135]	[a1,a2,a3,a4,a6]
Generators	[-5:9:1]	Generators of the group modulo torsion
j	19443408769/5883136	j-invariant
L	2.7904680859447	L(r)(E,1)/r!
Ω	1.7860118885518	Real period
R	0.065100072584236	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	7504r1 30016x1 8442a1 23450d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 938c1

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	-	-4	-3	0	4	-9	5	-7	-11	5	-8	6	6	10	-10	+	-5	-6	-2	-6	-12	-2

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Quadratic twists for elliptic curve 938c1

-4	8	-3	5	-7	-11	-67
7504r1	30016x1	8442a1	23450d1	6566i1	113498b1	62846a1

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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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