Cremona's table of elliptic curves

618 = 2 · 3 · 103

Field	Data	Notes
Atkin-Lehner	2- 3- 103+	Signs for the Atkin-Lehner involutions
Class	618f	Isogeny class
Conductor	618	Conductor
∏ cp	77	Product of Tamagawa factors cp
deg	616	Modular degree for the optimal curve
Δ	-461334528 = -1 · 211 · 37 · 103	Discriminant
Eigenvalues	2- 3- -4 -4 -3 -6  2  3	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-185,1401]	[a1,a2,a3,a4,a6]
Generators	[10:-29:1]	Generators of the group modulo torsion
j	-700463661841/461334528	j-invariant
L	2.6608279158632	L(r)(E,1)/r!
Ω	1.5379775186464	Real period
R	0.022468603266668	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	4944h1 19776c1 1854b1 15450i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 618f1

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
-	-	-4	-4	-3	-6	2	3	1	-5	-3	11	-12	6	-10	-4	0	8	-2	0	-4	-14	0	-9	-17

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Quadratic twists for elliptic curve 618f1

-4	8	-3	5	-7	-11	13	-103
4944h1	19776c1	1854b1	15450i1	30282bd1	74778t1	104442p1	63654h1

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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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