Cremona's table of elliptic curves

1984 = 2⁶ · 31

Field	Data	Notes
Atkin-Lehner	2+ 31+	Signs for the Atkin-Lehner involutions
Class	1984d	Isogeny class
Conductor	1984	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	125960192 = 217 · 312	Discriminant
Eigenvalues	2+  2 -2  0 -2 -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-129,-127]	[a1,a2,a3,a4,a6]
Generators	[17:48:1]	Generators of the group modulo torsion
j	1825346/961	j-invariant
L	3.5730400438021	L(r)(E,1)/r!
Ω	1.5015543267967	Real period
R	1.1897804761499	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	1984l2 248b2 17856p2 49600l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1984d2

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

---

Quadratic twists for elliptic curve 1984d2

-4	8	-3	5	-7	-31
1984l2	248b2	17856p2	49600l2	97216bb2	61504y2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations