Cremona's table of elliptic curves

3703 = 7 · 23²

Field	Data	Notes
Atkin-Lehner	7+ 23-	Signs for the Atkin-Lehner involutions
Class	3703a	Isogeny class
Conductor	3703	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2640	Modular degree for the optimal curve
Δ	23833778129 = 7 · 237	Discriminant
Eigenvalues	-1  0 -2 7+ -4  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1951,32806]	[a1,a2,a3,a4,a6]
j	5545233/161	j-invariant
L	0.29851149619758	L(r)(E,1)/r!
Ω	1.1940459847903	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	59248y1 33327g1 92575q1 25921b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3703a1

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	0	-2	+	-4	6	2	-4	-	-2	-4	2	-6	-12	-12	10	0	-2	-12	8	-14	-8	4	-6	10

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Quadratic twists for elliptic curve 3703a1

-4	-3	5	-7	-23
59248y1	33327g1	92575q1	25921b1	161a2

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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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