Cremona's table of elliptic curves

12320 = 2⁵ · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	12320g	Isogeny class
Conductor	12320	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	1897280 = 26 · 5 · 72 · 112	Discriminant
Eigenvalues	2-  2 5- 7+ 11+  0  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-330,2420]	[a1,a2,a3,a4,a6]
Generators	[2:42:1]	Generators of the group modulo torsion
j	62287505344/29645	j-invariant
L	6.6812287061307	L(r)(E,1)/r!
Ω	2.594684047978	Real period
R	1.2874840602148	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	12320m1 24640bh2 110880bb1 61600l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12320g1

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

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Quadratic twists for elliptic curve 12320g1

-4	8	-3	5	-7
12320m1	24640bh2	110880bb1	61600l1	86240be1

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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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