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	6325c	Isogeny class
Conductor	6325	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	3345925 = 52 · 11 · 233	Discriminant
Eigenvalues	0 -1 5+  1 11- -2 -3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1123,-14117]	[a1,a2,a3,a4,a6]
Generators	[-19:0:1]	Generators of the group modulo torsion
j	6270607851520/133837	j-invariant
L	2.552771457391	L(r)(E,1)/r!
Ω	0.82465623956524	Real period
R	1.0318527627693	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	101200q2 56925i2 6325f2 69575j2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6325c2

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	-1	+	1	-	-2	-3	-4	-	6	5	10	-6	1	0	-6	3	5	-8	9	-2	-1	12	-6	4

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Quadratic twists for elliptic curve 6325c2

-4	-3	5	-11
101200q2	56925i2	6325f2	69575j2

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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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