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	12705a	Isogeny class
Conductor	12705	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	48000	Modular degree for the optimal curve
Δ	-2426575758546555 = -1 · 35 · 5 · 7 · 1111	Discriminant
Eigenvalues	0 3+ 5+ 7+ 11-  0 -3  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-15891,-2487013]	[a1,a2,a3,a4,a6]
j	-250523582464/1369738755	j-invariant
L	0.76435584412365	L(r)(E,1)/r!
Ω	0.19108896103091	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	38115w1 63525bq1 88935ce1 1155d1	Quadratic twists by: -3 5 -7 -11

Hecke Eigenvalues for elliptic curve 12705a1

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
0	+	+	+	-	0	-3	3	-1	7	6	-8	2	5	-6	-3	-5	7	6	-10	-12	16	3	3	-1

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Quadratic twists for elliptic curve 12705a1

-3	5	-7	-11
38115w1	63525bq1	88935ce1	1155d1

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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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