Cremona's table of elliptic curves

27600 = 2⁴ · 3 · 5² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 23-	Signs for the Atkin-Lehner involutions
Class	27600dg	Isogeny class
Conductor	27600	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	76800	Modular degree for the optimal curve
Δ	-114264000000000 = -1 · 212 · 33 · 59 · 232	Discriminant
Eigenvalues	2- 3- 5-  2  0 -4 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-14208,825588]	[a1,a2,a3,a4,a6]
Generators	[42:-552:1]	Generators of the group modulo torsion
j	-39651821/14283	j-invariant
L	7.1526186945572	L(r)(E,1)/r!
Ω	0.55718048166261	Real period
R	1.0697638871002	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	1725i1 110400he1 82800fg1 27600bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600dg1

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	-4	-2	4	-	10	-4	-2	-10	2	8	-10	-6	-6	-10	-10	8	-16	0	4	2

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Quadratic twists for elliptic curve 27600dg1

-4	8	-3	5
1725i1	110400he1	82800fg1	27600bv1

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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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