Cremona's table of elliptic curves

23088 = 2⁴ · 3 · 13 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3- 13+ 37-	Signs for the Atkin-Lehner involutions
Class	23088g	Isogeny class
Conductor	23088	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	207584208 = 24 · 36 · 13 · 372	Discriminant
Eigenvalues	2+ 3-  0  0  2 13+  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5923,173492]	[a1,a2,a3,a4,a6]
Generators	[-4:444:1]	Generators of the group modulo torsion
j	1436488814848000/12974013	j-invariant
L	6.7971162995879	L(r)(E,1)/r!
Ω	1.6042730084859	Real period
R	1.4122941801124	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	11544g1 92352bs1 69264g1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 23088g1

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

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Quadratic twists for elliptic curve 23088g1

-4	8	-3
11544g1	92352bs1	69264g1

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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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