Cremona's table of elliptic curves

112 = 2⁴ · 7

Field	Data	Notes
Atkin-Lehner	2- 7+	Signs for the Atkin-Lehner involutions
Class	112c	Isogeny class
Conductor	112	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-89915392 = -1 · 218 · 73	Discriminant
Eigenvalues	2-  2  0 7+  0 -4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,72,368]	[a1,a2,a3,a4,a6]
j	9938375/21952	j-invariant
L	1.3254912396825	L(r)(E,1)/r!
Ω	1.3254912396825	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	14a1 448f3 1008i3 2800v3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 112c3

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	0	+	0	-4	6	-2	0	-6	4	2	6	-8	12	6	6	8	4	0	2	-8	6	-6	-10

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Quadratic twists for elliptic curve 112c3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
14a1	448f3	1008i3	2800v3	784j3	13552ba3	18928z3	32368bd3	40432r3	59248bb3	94192v3	107632i3

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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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