Cremona's table of elliptic curves

7744 = 2⁶ · 11²

Field	Data	Notes
Atkin-Lehner	2- 11-	Signs for the Atkin-Lehner involutions
Class	7744bg	Isogeny class
Conductor	7744	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-507510784 = -1 · 222 · 112	Discriminant
Eigenvalues	2- -2  3  2 11-  5 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,191,-321]	[a1,a2,a3,a4,a6]
Generators	[5:28:1]	Generators of the group modulo torsion
j	24167/16	j-invariant
L	3.9554372143843	L(r)(E,1)/r!
Ω	0.94099692386806	Real period
R	2.101726963211	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	7744k1 1936i1 69696gw1 7744bh1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7744bg1

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	3	2	-	5	-3	-2	-6	-3	-2	7	-3	-8	-6	3	0	-10	-10	-12	-14	2	-18	-9	11

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Quadratic twists for elliptic curve 7744bg1

-4	8	-3	-11
7744k1	1936i1	69696gw1	7744bh1

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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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