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	754c	Isogeny class
Conductor	754	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-568516 = -1 · 22 · 132 · 292	Discriminant
Eigenvalues	2+ -2 -2  2  0 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,13,-30]	[a1,a2,a3,a4,a6]
Generators	[5:10:1]	Generators of the group modulo torsion
j	270840023/568516	j-invariant
L	1.2261926627233	L(r)(E,1)/r!
Ω	1.5143025121498	Real period
R	0.40487044460571	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6032h2 24128c2 6786o2 18850s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 754c2

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	-2	2	0	-	2	4	-4	-	-8	6	-6	2	-8	-6	-10	-10	-2	-6	6	-14	-6	10	18

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Quadratic twists for elliptic curve 754c2

-4	8	-3	5	-7	-11	13	29
6032h2	24128c2	6786o2	18850s2	36946i2	91234s2	9802g2	21866k2

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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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