Cremona's table of elliptic curves

1232 = 2⁴ · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 7+ 11+	Signs for the Atkin-Lehner involutions
Class	1232a	Isogeny class
Conductor	1232	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-16696064 = -1 · 28 · 72 · 113	Discriminant
Eigenvalues	2+  1 -1 7+ 11+  0 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1,-197]	[a1,a2,a3,a4,a6]
Generators	[6:7:1]	Generators of the group modulo torsion
j	-1024/65219	j-invariant
L	2.7754637046892	L(r)(E,1)/r!
Ω	1.0031018247641	Real period
R	1.38344066184	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	616d1 4928y1 11088o1 30800i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1232a1

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
+	1	-1	+	+	0	-2	2	7	-10	-7	-9	-2	4	-8	2	15	-14	-3	-3	10	-10	0	-11	7

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Quadratic twists for elliptic curve 1232a1

-4	8	-3	5	-7	-11
616d1	4928y1	11088o1	30800i1	8624b1	13552f1

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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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