Cremona's table of elliptic curves

2698 = 2 · 19 · 71

Field	Data	Notes
Atkin-Lehner	2+ 19+ 71+	Signs for the Atkin-Lehner involutions
Class	2698a	Isogeny class
Conductor	2698	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	49038848 = 29 · 19 · 712	Discriminant
Eigenvalues	2+  0  2 -2  4 -6  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-51881,-4535475]	[a1,a2,a3,a4,a6]
Generators	[993142125:-5977510865:3581577]	Generators of the group modulo torsion
j	15443773948047428073/49038848	j-invariant
L	2.5423017924125	L(r)(E,1)/r!
Ω	0.31633487754707	Real period
R	16.07348397449	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	21584e2 86336f2 24282i2 67450k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2698a2

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	2	-2	4	-6	2	+	6	-2	4	-6	8	-4	6	-6	-14	-8	-2	+	-6	-16	-12	14	-16

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Quadratic twists for elliptic curve 2698a2

-4	8	-3	5	-19
21584e2	86336f2	24282i2	67450k2	51262h2

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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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