Cremona's table of elliptic curves

33810 = 2 · 3 · 5 · 7² · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7- 23-	Signs for the Atkin-Lehner involutions
Class	33810cq	Isogeny class
Conductor	33810	Conductor
∏ cp	144	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	639009000000 = 26 · 34 · 56 · 73 · 23	Discriminant
Eigenvalues	2- 3+ 5- 7- -4 -4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2605,32675]	[a1,a2,a3,a4,a6]
Generators	[-7:-222:1]	Generators of the group modulo torsion
j	5699846954647/1863000000	j-invariant
L	6.9740538329431	L(r)(E,1)/r!
Ω	0.84099589685809	Real period
R	0.23035037186922	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	101430ba1 33810cz1	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 33810cq1

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
-	+	-	-	-4	-4	-2	0	-	-2	4	-2	8	-2	-6	-6	10	6	14	12	10	-6	12	-2	18

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Quadratic twists for elliptic curve 33810cq1

-3	-7
101430ba1	33810cz1

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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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