Cremona's table of elliptic curves

6762 = 2 · 3 · 7² · 23

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 23-	Signs for the Atkin-Lehner involutions
Class	6762f	Isogeny class
Conductor	6762	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	230400	Modular degree for the optimal curve
Δ	-3.8170059896287E+19	Discriminant
Eigenvalues	2+ 3+  0 7-  6 -2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,227580,-294201648]	[a1,a2,a3,a4,a6]
Generators	[4424:293292:1]	Generators of the group modulo torsion
j	11079872671250375/324440155855872	j-invariant
L	2.7684352077106	L(r)(E,1)/r!
Ω	0.098967053083637	Real period
R	4.6622169052749	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	54096cq1 20286by1 966f1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 6762f1

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	-	6	-2	6	-2	-	-6	-8	8	-6	2	0	-12	0	-8	-10	0	-14	8	-6	-6	10

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Quadratic twists for elliptic curve 6762f1

-4	-3	-7
54096cq1	20286by1	966f1

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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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