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	12	Product of Tamagawa factors cp
Δ	-16141442800 = -1 · 24 · 52 · 79	Discriminant
Eigenvalues	2- -2 5+ 7-  3 -4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4818,127273]	[a1,a2,a3,a4,a6]
Generators	[2:343:1]	Generators of the group modulo torsion
j	-262885120/343	j-invariant
L	2.6183310178255	L(r)(E,1)/r!
Ω	1.2357077590527	Real period
R	0.17657431531605	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	19600cs2 78400ci2 44100cf2 4900t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4900m2

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 4900m2

-4	8	-3	5	-7
19600cs2	78400ci2	44100cf2	4900t2	700b2

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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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