Cremona's table of elliptic curves

3136 = 2⁶ · 7²

Field	Data	Notes
Atkin-Lehner	2- 7-	Signs for the Atkin-Lehner involutions
Class	3136z	Isogeny class
Conductor	3136	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-3373232128 = -1 · 212 · 77	Discriminant
Eigenvalues	2-  2  0 7- -4 -4  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,327,-1735]	[a1,a2,a3,a4,a6]
Generators	[23:132:1]	Generators of the group modulo torsion
j	8000/7	j-invariant
L	4.4137275427909	L(r)(E,1)/r!
Ω	0.77657554715371	Real period
R	2.8417889019091	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3136ba1 1568e1 28224ff1 78400iu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3136z1

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	0	-	-4	-4	2	6	-8	-2	-4	-10	10	4	4	2	-10	-8	-8	0	6	16	-2	-18	2

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Quadratic twists for elliptic curve 3136z1

-4	8	-3	5	-7
3136ba1	1568e1	28224ff1	78400iu1	448g1

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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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