Cremona's table of elliptic curves

15624 = 2³ · 3² · 7 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 31+	Signs for the Atkin-Lehner involutions
Class	15624f	Isogeny class
Conductor	15624	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-323979264 = -1 · 211 · 36 · 7 · 31	Discriminant
Eigenvalues	2+ 3- -1 7+ -4  4 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3,-866]	[a1,a2,a3,a4,a6]
j	-2/217	j-invariant
L	0.78398268523053	L(r)(E,1)/r!
Ω	0.78398268523053	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	31248v1 124992bf1 1736a1 109368s1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 15624f1

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	+	-4	4	-2	-2	-7	-1	+	-2	-8	6	-1	6	-8	4	3	-16	3	-3	1	9	8

---

Quadratic twists for elliptic curve 15624f1

-4	8	-3	-7
31248v1	124992bf1	1736a1	109368s1

---

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