Cremona's table of elliptic curves

12012 = 2² · 3 · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 11- 13-	Signs for the Atkin-Lehner involutions
Class	12012c	Isogeny class
Conductor	12012	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	81600	Modular degree for the optimal curve
Δ	-22458395794122288 = -1 · 24 · 35 · 710 · 112 · 132	Discriminant
Eigenvalues	2- 3+ -2 7+ 11- 13-  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-63029,9459378]	[a1,a2,a3,a4,a6]
j	-1730740156295544832/1403649737132643	j-invariant
L	0.69880353478569	L(r)(E,1)/r!
Ω	0.34940176739284	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48048cu1 36036f1 84084x1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12012c1

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	-8	2	-6	4	-2	6	8	2	-6	-6	2	-12	-8	-2	-4	-2	10	2

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Quadratic twists for elliptic curve 12012c1

-4	-3	-7
48048cu1	36036f1	84084x1

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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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