Cremona's table of elliptic curves

2553 = 3 · 23 · 37

Field	Data	Notes
Atkin-Lehner	3+ 23- 37+	Signs for the Atkin-Lehner involutions
Class	2553a	Isogeny class
Conductor	2553	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	616	Modular degree for the optimal curve
Δ	-1861137 = -1 · 37 · 23 · 37	Discriminant
Eigenvalues	1 3+  4  1  0  0 -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-173,810]	[a1,a2,a3,a4,a6]
j	-577801395289/1861137	j-invariant
L	2.6474415453276	L(r)(E,1)/r!
Ω	2.6474415453276	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40848k1 7659a1 63825m1 125097k1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2553a1

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
1	+	4	1	0	0	-2	6	-	-1	1	+	0	12	-13	6	12	3	8	-1	-1	2	-2	-6	-7

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Quadratic twists for elliptic curve 2553a1

-4	-3	5	-7	-23	37
40848k1	7659a1	63825m1	125097k1	58719c1	94461b1

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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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