Cremona's table of elliptic curves

35400 = 2³ · 3 · 5² · 59

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 59-	Signs for the Atkin-Lehner involutions
Class	35400f	Isogeny class
Conductor	35400	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	41472	Modular degree for the optimal curve
Δ	-127440000000 = -1 · 210 · 33 · 57 · 59	Discriminant
Eigenvalues	2+ 3- 5+  1  2  5 -1 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4008,-100512]	[a1,a2,a3,a4,a6]
Generators	[228:3300:1]	Generators of the group modulo torsion
j	-445138564/7965	j-invariant
L	7.9050188862561	L(r)(E,1)/r!
Ω	0.29968674624067	Real period
R	2.1981338251295	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	70800b1 106200bd1 7080i1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 35400f1

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	2	5	-1	-6	-3	8	-3	10	-6	-8	-11	-3	-	-12	-2	13	-7	4	-9	-13	-18

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Quadratic twists for elliptic curve 35400f1

-4	-3	5
70800b1	106200bd1	7080i1

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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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