Cremona's table of elliptic curves

2622 = 2 · 3 · 19 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 19+ 23-	Signs for the Atkin-Lehner involutions
Class	2622b	Isogeny class
Conductor	2622	Conductor
∏ cp	88	Product of Tamagawa factors cp
deg	11616	Modular degree for the optimal curve
Δ	-25387648155648 = -1 · 222 · 36 · 192 · 23	Discriminant
Eigenvalues	2- 3+ -2 -2  6 -6  4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-18259,972497]	[a1,a2,a3,a4,a6]
Generators	[-29:1230:1]	Generators of the group modulo torsion
j	-673218690226274737/25387648155648	j-invariant
L	3.5898407541628	L(r)(E,1)/r!
Ω	0.66610444694837	Real period
R	0.24496845874881	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	20976k1 83904q1 7866f1 65550u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2622b1

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	-2	6	-6	4	+	-	2	-4	-8	-2	8	-8	-6	4	8	-8	-8	-10	-2	-6	-8	-6

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Quadratic twists for elliptic curve 2622b1

-4	8	-3	5	-7	-19	-23
20976k1	83904q1	7866f1	65550u1	128478da1	49818q1	60306r1

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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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