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	12705f	Isogeny class
Conductor	12705	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	-51153823875 = -1 · 3 · 53 · 7 · 117	Discriminant
Eigenvalues	2 3+ 5- 7+ 11-  2  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-40,-10869]	[a1,a2,a3,a4,a6]
Generators	[186:117:8]	Generators of the group modulo torsion
j	-4096/28875	j-invariant
L	8.1447132600402	L(r)(E,1)/r!
Ω	0.51157576305806	Real period
R	2.6534724825356	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	38115o1 63525bx1 88935bt1 1155g1	Quadratic twists by: -3 5 -7 -11

Hecke Eigenvalues for elliptic curve 12705f1

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
2	+	-	+	-	2	3	-1	-7	-1	8	-2	8	-9	-12	-5	3	-13	-14	8	8	14	-11	-9	5

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Quadratic twists for elliptic curve 12705f1

-3	5	-7	-11
38115o1	63525bx1	88935bt1	1155g1

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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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