Cremona's table of elliptic curves

703 = 19 · 37

Field	Data	Notes
Atkin-Lehner	19- 37-	Signs for the Atkin-Lehner involutions
Class	703b	Isogeny class
Conductor	703	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	56	Modular degree for the optimal curve
Δ	-26011 = -1 · 19 · 372	Discriminant
Eigenvalues	-2  0 -3  3 -1  2  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,1,-8]	[a1,a2,a3,a4,a6]
Generators	[7:18:1]	Generators of the group modulo torsion
j	110592/26011	j-invariant
L	1.1006854339595	L(r)(E,1)/r!
Ω	1.7712720083193	Real period
R	0.31070480106665	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	11248h1 44992b1 6327d1 17575b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 703b1

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
-2	0	-3	3	-1	2	3	-	0	-4	0	-	-6	-3	-11	-2	-6	5	6	-10	-11	-14	-12	4	-14

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Quadratic twists for elliptic curve 703b1

-4	8	-3	5	-7	-11	13	-19	37
11248h1	44992b1	6327d1	17575b1	34447i1	85063e1	118807b1	13357b1	26011c1

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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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