Cremona's table of elliptic curves

7942 = 2 · 11 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 11- 19-	Signs for the Atkin-Lehner involutions
Class	7942g	Isogeny class
Conductor	7942	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	5040	Modular degree for the optimal curve
Δ	28139474924 = 22 · 117 · 192	Discriminant
Eigenvalues	2+  0  1  1 11- -2  0 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-989,-8599]	[a1,a2,a3,a4,a6]
Generators	[40:101:1]	Generators of the group modulo torsion
j	296518892481/77948684	j-invariant
L	3.2536773655603	L(r)(E,1)/r!
Ω	0.86792499980454	Real period
R	0.26777143896511	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	63536q1 71478bv1 87362bf1 7942p1	Quadratic twists by: -4 -3 -11 -19

Hecke Eigenvalues for elliptic curve 7942g1

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	1	1	-	-2	0	-	-6	8	10	-3	2	-8	0	9	14	0	-12	-6	0	11	7	-14	-5

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Quadratic twists for elliptic curve 7942g1

-4	-3	-11	-19
63536q1	71478bv1	87362bf1	7942p1

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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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