Cremona's table of elliptic curves

32340 = 2² · 3 · 5 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	32340c	Isogeny class
Conductor	32340	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	93312	Modular degree for the optimal curve
Δ	-69320101158000 = -1 · 24 · 312 · 53 · 72 · 113	Discriminant
Eigenvalues	2- 3+ 5+ 7- 11+ -5 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,474,400401]	[a1,a2,a3,a4,a6]
Generators	[48:-729:1]	Generators of the group modulo torsion
j	14990845184/88418496375	j-invariant
L	3.1836730617717	L(r)(E,1)/r!
Ω	0.48556458790053	Real period
R	1.0927736292636	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	129360gw1 97020dd1 32340bi1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 32340c1

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
-	+	+	-	+	-5	-6	-2	-6	0	7	2	0	-1	-6	6	3	10	2	15	-11	14	-3	3	10

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Quadratic twists for elliptic curve 32340c1

-4	-3	-7
129360gw1	97020dd1	32340bi1

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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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