Cremona's table of elliptic curves

7514 = 2 · 13 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 13- 17+	Signs for the Atkin-Lehner involutions
Class	7514d	Isogeny class
Conductor	7514	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	13284752 = 24 · 132 · 173	Discriminant
Eigenvalues	2+ -2 -4 -2 -2 13- 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-83,222]	[a1,a2,a3,a4,a6]
Generators	[-9:20:1] [-2:20:1]	Generators of the group modulo torsion
j	12649337/2704	j-invariant
L	2.4316873894306	L(r)(E,1)/r!
Ω	2.1149525772635	Real period
R	0.57487988515038	Regulator
r	2	Rank of the group of rational points
S	0.99999999999961	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	60112y1 67626bi1 97682p1 7514c1	Quadratic twists by: -4 -3 13 17

Hecke Eigenvalues for elliptic curve 7514d1

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	-4	-2	-2	-	+	4	-6	0	2	-4	-12	-4	8	-6	-12	8	-12	-6	12	-6	-12	-6	-12

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Quadratic twists for elliptic curve 7514d1

-4	-3	13	17
60112y1	67626bi1	97682p1	7514c1

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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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