Cremona's table of elliptic curves

3248 = 2⁴ · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 7+ 29-	Signs for the Atkin-Lehner involutions
Class	3248k	Isogeny class
Conductor	3248	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-78319517696 = -1 · 216 · 72 · 293	Discriminant
Eigenvalues	2- -1 -3 7+  3 -1  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-232,-13456]	[a1,a2,a3,a4,a6]
Generators	[58:406:1]	Generators of the group modulo torsion
j	-338608873/19120976	j-invariant
L	2.2619477870868	L(r)(E,1)/r!
Ω	0.47695071912233	Real period
R	0.39520990611098	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	406b1 12992x1 29232bb1 81200bu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3248k1

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	-1	0	4	6	-	-5	2	0	7	3	-9	-12	-10	-2	12	8	-5	-12	6	8

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Quadratic twists for elliptic curve 3248k1

-4	8	-3	5	-7	29
406b1	12992x1	29232bb1	81200bu1	22736bi1	94192o1

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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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