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	754b	Isogeny class
Conductor	754	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1248	Modular degree for the optimal curve
Δ	-75322597376 = -1 · 213 · 13 · 294	Discriminant
Eigenvalues	2+  1  1 -1 -6 13- -7 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-10758,428760]	[a1,a2,a3,a4,a6]
Generators	[60:-16:1]	Generators of the group modulo torsion
j	-137676653031953881/75322597376	j-invariant
L	1.9362290724353	L(r)(E,1)/r!
Ω	1.0757562718168	Real period
R	0.44996927351522	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	6032g1 24128b1 6786n1 18850p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 754b1

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	1	-1	-6	-	-7	-2	-4	-	4	9	12	-1	7	0	-10	-4	-2	-3	6	4	0	-14	6

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Quadratic twists for elliptic curve 754b1

-4	8	-3	5	-7	-11	13	29
6032g1	24128b1	6786n1	18850p1	36946g1	91234q1	9802f1	21866g1

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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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