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
deg	1344	Modular degree for the optimal curve
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,-457,-559]	[a1,a2,a3,a4,a6]
Generators	[-16:49:1]	Generators of the group modulo torsion
j	1792	j-invariant
L	2.3246761005324	L(r)(E,1)/r!
Ω	1.1082307607593	Real period
R	0.69921541699482	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	3136o1 196b1 28224bf1 78400c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3136b1

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 3136b1

-4	8	-3	5	-7
3136o1	196b1	28224bf1	78400c1	3136f1

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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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