Cremona's table of elliptic curves

4704 = 2⁵ · 3 · 7²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7-	Signs for the Atkin-Lehner involutions
Class	4704t	Isogeny class
Conductor	4704	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	43680	Modular degree for the optimal curve
Δ	-230582674642650624 = -1 · 29 · 313 · 710	Discriminant
Eigenvalues	2- 3+ -1 7- -1  0  8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,152864,-2188556]	[a1,a2,a3,a4,a6]
Generators	[6180:486758:1]	Generators of the group modulo torsion
j	2731405432/1594323	j-invariant
L	2.9862549923704	L(r)(E,1)/r!
Ω	0.18513089270804	Real period
R	8.0652530452598	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	4704bb1 9408cs1 14112q1 117600ct1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4704t1

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	8	-4	-4	-5	7	8	-4	-10	6	-1	9	2	-2	-6	-2	9	-3	6	1

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Quadratic twists for elliptic curve 4704t1

-4	8	-3	5	-7
4704bb1	9408cs1	14112q1	117600ct1	4704z1

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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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