Cremona's table of elliptic curves

1957 = 19 · 103

Field	Data	Notes
Atkin-Lehner	19- 103+	Signs for the Atkin-Lehner involutions
Class	1957a	Isogeny class
Conductor	1957	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	880	Modular degree for the optimal curve
Δ	255038197 = 195 · 103	Discriminant
Eigenvalues	1 -1 -4 -1 -4 -4 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-522,4315]	[a1,a2,a3,a4,a6]
Generators	[6:35:1] [18:25:1]	Generators of the group modulo torsion
j	15777367606441/255038197	j-invariant
L	3.0571158373031	L(r)(E,1)/r!
Ω	1.7531598663554	Real period
R	0.34875494197328	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	31312p1 125248b1 17613e1 48925b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1957a1

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	-1	-4	-4	-2	-	-5	2	-5	-5	0	-2	-4	3	10	-15	1	-11	-10	-14	9	11	-10

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Quadratic twists for elliptic curve 1957a1

-4	8	-3	5	-7	-19
31312p1	125248b1	17613e1	48925b1	95893b1	37183b1

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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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