Cremona's table of elliptic curves

9912 = 2³ · 3 · 7 · 59

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 59-	Signs for the Atkin-Lehner involutions
Class	9912d	Isogeny class
Conductor	9912	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	168960	Modular degree for the optimal curve
Δ	61697858521162752 = 210 · 311 · 78 · 59	Discriminant
Eigenvalues	2+ 3+  0 7-  4  0  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3477488,2497142364]	[a1,a2,a3,a4,a6]
Generators	[-1670:60368:1]	Generators of the group modulo torsion
j	4541724645902232578500/60251814962073	j-invariant
L	4.1701879056291	L(r)(E,1)/r!
Ω	0.31914917756332	Real period
R	3.2666447219668	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	19824e1 79296w1 29736s1 69384j1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9912d1

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	-	4	0	6	-4	-4	0	2	-4	-2	-8	-4	-4	-	-4	4	2	2	-16	-12	-6	-18

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Quadratic twists for elliptic curve 9912d1

-4	8	-3	-7
19824e1	79296w1	29736s1	69384j1

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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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