Cremona's table of elliptic curves

12675 = 3 · 5² · 13²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	12675j	Isogeny class
Conductor	12675	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	338688	Modular degree for the optimal curve
Δ	-2068127391357421875 = -1 · 33 · 513 · 137	Discriminant
Eigenvalues	2 3+ 5+ -1 -5 13+  7  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-280258,-89619957]	[a1,a2,a3,a4,a6]
Generators	[12291246:356922801:10648]	Generators of the group modulo torsion
j	-32278933504/27421875	j-invariant
L	7.2628934443981	L(r)(E,1)/r!
Ω	0.10016155081859	Real period
R	9.0639738814949	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	38025bq1 2535k1 975d1	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 12675j1

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	+	+	-1	-5	+	7	6	-3	2	-2	7	-9	8	10	-5	0	5	-4	-9	-6	-3	-4	-11	-11

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Quadratic twists for elliptic curve 12675j1

-3	5	13
38025bq1	2535k1	975d1

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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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