Cremona's table of elliptic curves

6325 = 5² · 11 · 23

Field	Data	Notes
Atkin-Lehner	5+ 11- 23-	Signs for the Atkin-Lehner involutions
Class	6325d	Isogeny class
Conductor	6325	Conductor
∏ cp	5	Product of Tamagawa factors cp
Δ	36173564453125 = 510 · 115 · 23	Discriminant
Eigenvalues	-2 -1 5+  3 11- -6  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-68958,-6940932]	[a1,a2,a3,a4,a6]
Generators	[-149:60:1]	Generators of the group modulo torsion
j	3713504358400/3704173	j-invariant
L	1.7262899846036	L(r)(E,1)/r!
Ω	0.29463129470475	Real period
R	1.1718307020532	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	101200t2 56925n2 6325g1 69575r2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6325d2

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	-1	+	3	-	-6	3	0	-	0	-3	-2	2	-1	8	4	-5	-13	8	-3	14	5	4	0	-2

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Quadratic twists for elliptic curve 6325d2

-4	-3	5	-11
101200t2	56925n2	6325g1	69575r2

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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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