Cremona's table of elliptic curves

11970 = 2 · 3² · 5 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7+ 19+	Signs for the Atkin-Lehner involutions
Class	11970bj	Isogeny class
Conductor	11970	Conductor
∏ cp	560	Product of Tamagawa factors cp
deg	26880	Modular degree for the optimal curve
Δ	-24453273600000 = -1 · 214 · 33 · 55 · 72 · 192	Discriminant
Eigenvalues	2- 3+ 5- 7+  0 -2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,7138,50349]	[a1,a2,a3,a4,a6]
Generators	[17:411:1]	Generators of the group modulo torsion
j	1489863969861597/905676800000	j-invariant
L	7.2046460995893	L(r)(E,1)/r!
Ω	0.41378573937814	Real period
R	0.12436812813208	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	95760cw1 11970a1 59850o1 83790cu1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 11970bj1

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	-2	2	+	-4	4	-4	-2	-10	2	-12	2	-10	-10	8	4	2	4	4	10	-8

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Quadratic twists for elliptic curve 11970bj1

-4	-3	5	-7
95760cw1	11970a1	59850o1	83790cu1

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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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