Cremona's table of elliptic curves

111600 = 2⁴ · 3² · 5² · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 31+	Signs for the Atkin-Lehner involutions
Class	111600dd	Isogeny class
Conductor	111600	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	614400	Modular degree for the optimal curve
Δ	-3321216000000000 = -1 · 216 · 33 · 59 · 312	Discriminant
Eigenvalues	2- 3+ 5-  2  4  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-247875,47581250]	[a1,a2,a3,a4,a6]
Generators	[289:288:1]	Generators of the group modulo torsion
j	-7797729087/15376	j-invariant
L	8.0001161979178	L(r)(E,1)/r!
Ω	0.44734177831098	Real period
R	2.2354597082058	Regulator
r	1	Rank of the group of rational points
S	1.0000000035283	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13950l1 111600de1 111600df1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 111600dd1

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

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Quadratic twists for elliptic curve 111600dd1

-4	-3	5
13950l1	111600de1	111600df1

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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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