Cremona's table of elliptic curves

22704 = 2⁴ · 3 · 11 · 43

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11+ 43+	Signs for the Atkin-Lehner involutions
Class	22704b	Isogeny class
Conductor	22704	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	74173968 = 24 · 34 · 113 · 43	Discriminant
Eigenvalues	2+ 3+  0 -3 11+ -2 -2  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-148,-509]	[a1,a2,a3,a4,a6]
Generators	[-5:9:1]	Generators of the group modulo torsion
j	22559008000/4635873	j-invariant
L	3.313929649252	L(r)(E,1)/r!
Ω	1.3877786028242	Real period
R	1.1939691397849	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11352o1 90816cr1 68112n1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 22704b1

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	-3	+	-2	-2	3	-1	-5	5	0	-4	+	3	11	5	-1	7	12	14	10	8	0	-15

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Quadratic twists for elliptic curve 22704b1

-4	8	-3
11352o1	90816cr1	68112n1

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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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