Cremona's table of elliptic curves

7744 = 2⁶ · 11²

Field	Data	Notes
Atkin-Lehner	2+ 11-	Signs for the Atkin-Lehner involutions
Class	7744m	Isogeny class
Conductor	7744	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-56192894500864 = -1 · 218 · 118	Discriminant
Eigenvalues	2+ -2 -1 -2 11- -1 -5 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-232481,43068991]	[a1,a2,a3,a4,a6]
Generators	[-323:9196:1] [243:992:1]	Generators of the group modulo torsion
j	-24729001	j-invariant
L	3.8803502187704	L(r)(E,1)/r!
Ω	0.58907542846582	Real period
R	0.54893228032448	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7744bb2 121c2 69696bq2 7744l1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7744m2

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	-1	-2	-	-1	-5	-6	2	-9	-2	3	-5	0	2	-9	-8	-6	-2	12	-2	-10	-6	-9	-13

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Quadratic twists for elliptic curve 7744m2

-4	8	-3	-11
7744bb2	121c2	69696bq2	7744l1

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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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