Cremona's table of elliptic curves

1957 = 19 · 103

Field	Data	Notes
Atkin-Lehner	19- 103+	Signs for the Atkin-Lehner involutions
Class	1957b	Isogeny class
Conductor	1957	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	1957 = 19 · 103	Discriminant
Eigenvalues	-1 -1  0 -5  0 -4 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-8,-12]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1] [4:4:1]	Generators of the group modulo torsion
j	57066625/1957	j-invariant
L	1.961306046964	L(r)(E,1)/r!
Ω	2.8428787702709	Real period
R	0.68990140116896	Regulator
r	2	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	31312o1 125248a1 17613b1 48925a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1957b1

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	0	-5	0	-4	-2	-	-9	-6	-5	-1	-8	-6	8	-1	-6	-7	9	-11	14	-10	5	-17	-2

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Quadratic twists for elliptic curve 1957b1

-4	8	-3	5	-7	-19
31312o1	125248a1	17613b1	48925a1	95893c1	37183a1

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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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