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	4	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-7168 = -1 · 210 · 7	Discriminant
Eigenvalues	2+ -2 -4 7+  0  0 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,0,4]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	-4/7	j-invariant
L	0.80930072859772	L(r)(E,1)/r!
Ω	3.3732121966451	Real period
R	0.2399198987252	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	56b1 448e1 1008f1 2800g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 112a1

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 112a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
56b1	448e1	1008f1	2800g1	784e1	13552i1	18928h1	32368e1	40432f1	59248p1	94192d1	107632b1

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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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