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	3248b	Isogeny class
Conductor	3248	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-248419720192 = -1 · 210 · 73 · 294	Discriminant
Eigenvalues	2+ -2  0 7+  0  4  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2128,-45468]	[a1,a2,a3,a4,a6]
Generators	[58:172:1]	Generators of the group modulo torsion
j	-1041220466500/242597383	j-invariant
L	2.3709213710769	L(r)(E,1)/r!
Ω	0.34715699625069	Real period
R	3.4147682412898	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	1624b1 12992bc1 29232f1 81200j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3248b1

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	+	0	4	2	-6	0	+	0	2	10	8	-8	6	-10	-12	12	-8	14	0	-2	-10	-14

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Quadratic twists for elliptic curve 3248b1

-4	8	-3	5	-7	29
1624b1	12992bc1	29232f1	81200j1	22736j1	94192c1

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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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