Cremona's table of elliptic curves

1870 = 2 · 5 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 5- 11- 17-	Signs for the Atkin-Lehner involutions
Class	1870h	Isogeny class
Conductor	1870	Conductor
∏ cp	1500	Product of Tamagawa factors cp
deg	48000	Modular degree for the optimal curve
Δ	-2128704136908800000 = -1 · 215 · 55 · 114 · 175	Discriminant
Eigenvalues	2- -1 5- -2 11- -1 17- -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2439835,1467522537]	[a1,a2,a3,a4,a6]
Generators	[-1773:15846:1]	Generators of the group modulo torsion
j	-1606220241149825308027441/2128704136908800000	j-invariant
L	3.6215667601731	L(r)(E,1)/r!
Ω	0.26019504929905	Real period
R	0.23197768814391	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	14960n1 59840c1 16830p1 9350f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1870h1

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	-	-2	-	-1	-	-5	-6	-5	7	-12	2	-6	-7	9	-5	-3	-2	-13	9	0	4	15	-17

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Quadratic twists for elliptic curve 1870h1

-4	8	-3	5	-7	-11	17
14960n1	59840c1	16830p1	9350f1	91630bp1	20570d1	31790n1

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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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