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	16	Product of Tamagawa factors cp
Δ	561280772 = 22 · 134 · 173	Discriminant
Eigenvalues	2+ -2 -4 -2 -2 13- 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-423,-3178]	[a1,a2,a3,a4,a6]
Generators	[-14:13:1] [-11:18:1]	Generators of the group modulo torsion
j	1697936057/114244	j-invariant
L	2.4316873894306	L(r)(E,1)/r!
Ω	1.0574762886318	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	60112y2 67626bi2 97682p2 7514c2	Quadratic twists by: -4 -3 13 17

Hecke Eigenvalues for elliptic curve 7514d2

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 7514d2

-4	-3	13	17
60112y2	67626bi2	97682p2	7514c2

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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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