Cremona's table of elliptic curves

1736 = 2³ · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 7+ 31-	Signs for the Atkin-Lehner involutions
Class	1736b	Isogeny class
Conductor	1736	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	6240	Modular degree for the optimal curve
Δ	-2154296356597504 = -1 · 28 · 710 · 313	Discriminant
Eigenvalues	2-  0  2 7+  2 -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12479,-2296670]	[a1,a2,a3,a4,a6]
Generators	[213:2170:1]	Generators of the group modulo torsion
j	-839504640199248/8415220142959	j-invariant
L	3.0356930157509	L(r)(E,1)/r!
Ω	0.19651554431221	Real period
R	2.5745995703763	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	3472b1 13888g1 15624k1 43400k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1736b1

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
-	0	2	+	2	-4	0	-4	-6	-6	-	10	2	-10	-8	6	-12	12	8	-8	-8	-14	-4	0	6

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Quadratic twists for elliptic curve 1736b1

-4	8	-3	5	-7	-31
3472b1	13888g1	15624k1	43400k1	12152d1	53816b1

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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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