Cremona's table of elliptic curves

1246 = 2 · 7 · 89

Field	Data	Notes
Atkin-Lehner	2+ 7- 89-	Signs for the Atkin-Lehner involutions
Class	1246f	Isogeny class
Conductor	1246	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	17444 = 22 · 72 · 89	Discriminant
Eigenvalues	2+  2 -2 7-  0 -4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-91,-375]	[a1,a2,a3,a4,a6]
Generators	[12:15:1]	Generators of the group modulo torsion
j	84778086457/17444	j-invariant
L	2.4195241296866	L(r)(E,1)/r!
Ω	1.5435650109137	Real period
R	1.5674909139424	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	9968j1 39872w1 11214q1 31150r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1246f1

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	-2	-	0	-4	-6	-2	0	4	-8	4	-2	10	0	-10	-14	4	0	0	6	0	-18	-	14

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Quadratic twists for elliptic curve 1246f1

-4	8	-3	5	-7	89
9968j1	39872w1	11214q1	31150r1	8722h1	110894e1

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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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