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	7514f	Isogeny class
Conductor	7514	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	5130585888766208 = 28 · 132 · 179	Discriminant
Eigenvalues	2-  0  4  2  2 13+ 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-49618,-2481711]	[a1,a2,a3,a4,a6]
j	559679941521/212556032	j-invariant
L	5.2841535492675	L(r)(E,1)/r!
Ω	0.33025959682922	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	60112o1 67626m1 97682c1 442b1	Quadratic twists by: -4 -3 13 17

Hecke Eigenvalues for elliptic curve 7514f1

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
-	0	4	2	2	+	+	0	4	-2	2	0	0	4	-8	-6	8	2	16	14	16	-8	-12	-18	4

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Quadratic twists for elliptic curve 7514f1

-4	-3	13	17
60112o1	67626m1	97682c1	442b1

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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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