Cremona's table of elliptic curves

112 = 2⁴ · 7

Field	Data	Notes
Atkin-Lehner	2+ 7-	Signs for the Atkin-Lehner involutions
Class	112b	Isogeny class
Conductor	112	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	14336 = 211 · 7	Discriminant
Eigenvalues	2+  0  2 7-  4  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-299,-1990]	[a1,a2,a3,a4,a6]
j	1443468546/7	j-invariant
L	1.1481057287391	L(r)(E,1)/r!
Ω	1.1481057287391	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	56a4 448b3 1008h4 2800a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 112b3

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	-	4	2	-6	-8	0	6	-8	-2	2	4	8	6	0	-6	4	8	10	-16	-8	-6	-6

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Quadratic twists for elliptic curve 112b3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
56a4	448b3	1008h4	2800a3	784c4	13552c4	18928b3	32368a4	40432j4	59248c4	94192i4	107632d4

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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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