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	12705p	Isogeny class
Conductor	12705	Conductor
∏ cp	100	Product of Tamagawa factors cp
deg	720000	Modular degree for the optimal curve
Δ	-3.0094051633627E+19	Discriminant
Eigenvalues	2 3- 5- 7+ 11-  6  7  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1081780,-507519941]	[a1,a2,a3,a4,a6]
j	-79028701534867456/16987307596875	j-invariant
L	7.3176198095069	L(r)(E,1)/r!
Ω	0.073176198095069	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	38115p1 63525v1 88935s1 1155n1	Quadratic twists by: -3 5 -7 -11

Hecke Eigenvalues for elliptic curve 12705p1

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	-	-	+	-	6	7	5	-1	5	-8	-2	-12	11	8	-11	-5	-7	-2	12	-4	10	1	15	3

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Quadratic twists for elliptic curve 12705p1

-3	5	-7	-11
38115p1	63525v1	88935s1	1155n1

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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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