Cremona's table of elliptic curves

20384 = 2⁵ · 7² · 13

Field	Data	Notes
Atkin-Lehner	2+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	20384d	Isogeny class
Conductor	20384	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	69120	Modular degree for the optimal curve
Δ	-2224223669437952 = -1 · 29 · 711 · 133	Discriminant
Eigenvalues	2+  1  0 7-  1 13+ -4  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,30952,-859048]	[a1,a2,a3,a4,a6]
j	54439939000/36924979	j-invariant
L	2.0963625947993	L(r)(E,1)/r!
Ω	0.26204532434992	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20384e1 40768dn1 2912c1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 20384d1

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	0	-	1	+	-4	6	-5	8	-1	-5	7	8	7	4	10	-7	-7	-12	-9	1	8	6	-19

---

Quadratic twists for elliptic curve 20384d1

-4	8	-7
20384e1	40768dn1	2912c1

---

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