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	12705c	Isogeny class
Conductor	12705	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	2363306663025 = 32 · 52 · 72 · 118	Discriminant
Eigenvalues	1 3+ 5+ 7- 11-  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-6778,-204497]	[a1,a2,a3,a4,a6]
Generators	[154:1483:1]	Generators of the group modulo torsion
j	19443408769/1334025	j-invariant
L	4.1756489444574	L(r)(E,1)/r!
Ω	0.52842919003537	Real period
R	3.9510014049166	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	38115bd2 63525bi2 88935cg2 1155a2	Quadratic twists by: -3 5 -7 -11

Hecke Eigenvalues for elliptic curve 12705c2

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	0	6	0	6	10	-4	8	-6	-8	-2	-8	-8	14	-4	16	-10	-2

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Quadratic twists for elliptic curve 12705c2

-3	5	-7	-11
38115bd2	63525bi2	88935cg2	1155a2

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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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