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	1246i	Isogeny class
Conductor	1246	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-279104 = -1 · 26 · 72 · 89	Discriminant
Eigenvalues	2- -1 -1 7+  0  4 -7  7	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-41,87]	[a1,a2,a3,a4,a6]
Generators	[1:6:1]	Generators of the group modulo torsion
j	-7633736209/279104	j-invariant
L	3.0232138172519	L(r)(E,1)/r!
Ω	3.0687979952249	Real period
R	0.082095493141943	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	9968m1 39872e1 11214d1 31150i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1246i1

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
-	-1	-1	+	0	4	-7	7	-9	-4	-7	2	-12	-5	2	-1	-12	10	-8	-2	13	-8	4	-	19

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Quadratic twists for elliptic curve 1246i1

-4	8	-3	5	-7	89
9968m1	39872e1	11214d1	31150i1	8722n1	110894s1

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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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