Cremona's table of elliptic curves

112 = 2⁴ · 7

Field	Data	Notes
Atkin-Lehner	2+ 7+	Signs for the Atkin-Lehner involutions
Class	112a	Isogeny class
Conductor	112	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	100352 = 211 · 72	Discriminant
Eigenvalues	2+ -2 -4 7+  0  0 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-40,84]	[a1,a2,a3,a4,a6]
Generators	[10:-28:1]	Generators of the group modulo torsion
j	3543122/49	j-invariant
L	0.80930072859772	L(r)(E,1)/r!
Ω	3.3732121966451	Real period
R	0.1199599493626	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	56b2 448e2 1008f2 2800g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 112a2

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	-4	+	0	0	-2	2	-8	2	-4	-6	-2	-8	4	-10	-6	4	12	0	-14	8	-6	10	-2

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Quadratic twists for elliptic curve 112a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
56b2	448e2	1008f2	2800g2	784e2	13552i2	18928h2	32368e2	40432f2	59248p2	94192d2	107632b2

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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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