Cremona's table of elliptic curves

6825 = 3 · 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	6825h	Isogeny class
Conductor	6825	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	325208896036171875 = 36 · 57 · 7 · 138	Discriminant
Eigenvalues	1 3- 5+ 7+  4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3416876,-2431168477]	[a1,a2,a3,a4,a6]
j	282352188585428161201/20813369346315	j-invariant
L	2.665050408329	L(r)(E,1)/r!
Ω	0.11104376701371	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	109200dt6 20475s5 1365b5 47775p6	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6825h5

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
1	-	+	+	4	+	-2	-4	0	-2	8	2	-6	4	0	2	12	14	-4	0	-10	0	12	-6	14

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Quadratic twists for elliptic curve 6825h5

-4	-3	5	-7	13
109200dt6	20475s5	1365b5	47775p6	88725bt6

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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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