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	1232f	Isogeny class
Conductor	1232	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-2207744 = -1 · 212 · 72 · 11	Discriminant
Eigenvalues	2- -1  3 7+ 11- -4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1429,-20323]	[a1,a2,a3,a4,a6]
Generators	[44:7:1]	Generators of the group modulo torsion
j	-78843215872/539	j-invariant
L	2.4916486789865	L(r)(E,1)/r!
Ω	0.38822723638015	Real period
R	3.2090080827645	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	77b3 4928t1 11088bj1 30800bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1232f1

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	3	+	-	-4	-6	-2	-3	-6	-5	11	6	-8	0	-6	9	-10	-5	-9	2	10	-12	-3	-1

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Quadratic twists for elliptic curve 1232f1

-4	8	-3	5	-7	-11
77b3	4928t1	11088bj1	30800bt1	8624bb1	13552z1

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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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