Cremona's table of elliptic curves

754 = 2 · 13 · 29

Field	Data	Notes
Atkin-Lehner	2- 13+ 29-	Signs for the Atkin-Lehner involutions
Class	754d	Isogeny class
Conductor	754	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-5597696 = -1 · 29 · 13 · 292	Discriminant
Eigenvalues	2-  1 -3 -3 -4 13+ -1  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,43,-31]	[a1,a2,a3,a4,a6]
Generators	[14:51:1]	Generators of the group modulo torsion
j	8780064047/5597696	j-invariant
L	2.9335184327792	L(r)(E,1)/r!
Ω	1.3796837741075	Real period
R	0.11812362319832	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	6032d1 24128h1 6786c1 18850f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 754d1

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	-3	-4	+	-1	0	2	-	4	-1	-2	3	3	-4	-12	10	-2	-5	0	-10	-6	10	-18

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Quadratic twists for elliptic curve 754d1

-4	8	-3	5	-7	-11	13	29
6032d1	24128h1	6786c1	18850f1	36946u1	91234k1	9802b1	21866a1

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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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