Cremona's table of elliptic curves

49 = 7²

Field	Data	Notes
Atkin-Lehner	7-	Signs for the Atkin-Lehner involutions
Class	49a	Isogeny class
Conductor	49	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	40353607 = 79	Discriminant
Eigenvalues	1  0  0 7-  4  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1822,30393]	[a1,a2,a3,a4,a6]
j	16581375	j-invariant
L	0.96665585280841	L(r)(E,1)/r!
Ω	1.9333117056168	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	784h4 3136d4 441d4 1225b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 49a4

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	0	-	4	0	0	0	8	2	0	-6	0	-12	0	-10	0	0	4	16	0	8	0	0	0

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Quadratic twists for elliptic curve 49a4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
784h4	3136d4	441d4	1225b4	49a2	5929e4	8281g4	14161a4	17689h4	25921a4	41209e4	47089a4	67081c4	82369a4	90601c4	108241a4

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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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