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	18	Product of Tamagawa factors cp
Δ	-473249533374464 = -1 · 212 · 72 · 119	Discriminant
Eigenvalues	2- -1  3 7+ 11- -4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,7051,1019197]	[a1,a2,a3,a4,a6]
Generators	[-36:847:1]	Generators of the group modulo torsion
j	9463555063808/115539436859	j-invariant
L	2.4916486789865	L(r)(E,1)/r!
Ω	0.38822723638015	Real period
R	0.35655645364051	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	77b2 4928t3 11088bj3 30800bt3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1232f3

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 1232f3

-4	8	-3	5	-7	-11
77b2	4928t3	11088bj3	30800bt3	8624bb3	13552z3

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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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