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	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	6032 = 24 · 13 · 29	Discriminant
Eigenvalues	2+ -2 -2  2  0 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-7,-6]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1]	Generators of the group modulo torsion
j	30664297/6032	j-invariant
L	1.2261926627233	L(r)(E,1)/r!
Ω	3.0286050242996	Real period
R	0.80974088921142	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	6032h1 24128c1 6786o1 18850s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 754c1

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 754c1

-4	8	-3	5	-7	-11	13	29
6032h1	24128c1	6786o1	18850s1	36946i1	91234s1	9802g1	21866k1

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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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