Cremona's table of elliptic curves

4900 = 2² · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	4900m	Isogeny class
Conductor	4900	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-329417200 = -1 · 24 · 52 · 77	Discriminant
Eigenvalues	2- -2 5+ 7-  3 -4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,82,853]	[a1,a2,a3,a4,a6]
Generators	[9:49:1]	Generators of the group modulo torsion
j	1280/7	j-invariant
L	2.6183310178255	L(r)(E,1)/r!
Ω	1.2357077590527	Real period
R	0.52972294594816	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	19600cs1 78400ci1 44100cf1 4900t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4900m1

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	+	-	3	-4	0	-2	3	9	-8	-5	6	-11	6	-6	0	10	-5	15	-10	-7	12	12	8

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Quadratic twists for elliptic curve 4900m1

-4	8	-3	5	-7
19600cs1	78400ci1	44100cf1	4900t1	700b1

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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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