Cremona's table of elliptic curves

12705 = 3 · 5 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	12705b	Isogeny class
Conductor	12705	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	34560	Modular degree for the optimal curve
Δ	1381153244625 = 34 · 53 · 7 · 117	Discriminant
Eigenvalues	-1 3+ 5+ 7+ 11-  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-24626,-1496626]	[a1,a2,a3,a4,a6]
Generators	[-92:74:1] [182:211:1]	Generators of the group modulo torsion
j	932288503609/779625	j-invariant
L	3.554312616977	L(r)(E,1)/r!
Ω	0.38112970285633	Real period
R	4.6628648860723	Regulator
r	2	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	38115z1 63525br1 88935ci1 1155c1	Quadratic twists by: -3 5 -7 -11

Hecke Eigenvalues for elliptic curve 12705b1

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

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Quadratic twists for elliptic curve 12705b1

-3	5	-7	-11
38115z1	63525br1	88935ci1	1155c1

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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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