Cremona's table of elliptic curves

12880 = 2⁴ · 5 · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 23+	Signs for the Atkin-Lehner involutions
Class	12880o	Isogeny class
Conductor	12880	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	571559483801600 = 228 · 52 · 7 · 233	Discriminant
Eigenvalues	2-  0 5+ 7-  2  0  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-21563,-402838]	[a1,a2,a3,a4,a6]
Generators	[319:5018:1]	Generators of the group modulo torsion
j	270701905514769/139540889600	j-invariant
L	4.3949174907132	L(r)(E,1)/r!
Ω	0.41658304775291	Real period
R	5.2749595961956	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	1610b1 51520cf1 115920fe1 64400bh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12880o1

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

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Quadratic twists for elliptic curve 12880o1

-4	8	-3	5	-7
1610b1	51520cf1	115920fe1	64400bh1	90160cl1

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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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