Cremona's table of elliptic curves

3136 = 2⁶ · 7²

Field	Data	Notes
Atkin-Lehner	2+ 7+	Signs for the Atkin-Lehner involutions
Class	3136b	Isogeny class
Conductor	3136	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	5903156224 = 210 · 78	Discriminant
Eigenvalues	2+ -1 -3 7+  3 -2  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-27897,-1784159]	[a1,a2,a3,a4,a6]
Generators	[-96:1:1]	Generators of the group modulo torsion
j	406749952	j-invariant
L	2.3246761005324	L(r)(E,1)/r!
Ω	0.36941025358644	Real period
R	2.0976462509845	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	3136o2 196b2 28224bf2 78400c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3136b2

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	-3	+	3	-2	3	1	3	6	-7	1	6	4	-9	-3	-9	1	7	0	-1	-13	-12	15	-10

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Quadratic twists for elliptic curve 3136b2

-4	8	-3	5	-7
3136o2	196b2	28224bf2	78400c2	3136f2

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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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