Cremona's table of elliptic curves

2898 = 2 · 3² · 7 · 23

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 23+	Signs for the Atkin-Lehner involutions
Class	2898a	Isogeny class
Conductor	2898	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	224	Modular degree for the optimal curve
Δ	-8694 = -1 · 2 · 33 · 7 · 23	Discriminant
Eigenvalues	2+ 3+ -1 7+  2 -1  6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-15,27]	[a1,a2,a3,a4,a6]
Generators	[3:0:1]	Generators of the group modulo torsion
j	-14348907/322	j-invariant
L	2.3230081649272	L(r)(E,1)/r!
Ω	4.1210761917801	Real period
R	0.28184484547515	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	23184be1 92736c1 2898k1 72450ct1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2898a1

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	+	2	-1	6	-6	+	5	-8	3	9	3	-9	-6	-8	2	4	10	2	-4	4	0	-5

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Quadratic twists for elliptic curve 2898a1

-4	8	-3	5	-7	-23
23184be1	92736c1	2898k1	72450ct1	20286f1	66654d1

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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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