Cremona's table of elliptic curves

38025 = 3² · 5² · 13²

Field	Data	Notes
Atkin-Lehner	3- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	38025bb	Isogeny class
Conductor	38025	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	774144	Modular degree for the optimal curve
Δ	289471654713515625 = 310 · 57 · 137	Discriminant
Eigenvalues	1 3- 5+  0  4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-4183542,-3292403009]	[a1,a2,a3,a4,a6]
j	147281603041/5265	j-invariant
L	3.8002918365143	L(r)(E,1)/r!
Ω	0.1055636621275	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12675e1 7605p1 2925g1	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 38025bb1

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	-	+	0	4	+	2	4	8	2	8	6	-6	4	8	6	-12	-2	-4	0	-6	16	4	10	18

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Quadratic twists for elliptic curve 38025bb1

-3	5	13
12675e1	7605p1	2925g1

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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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