Cremona's table of elliptic curves

31824 = 2⁴ · 3² · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	31824b	Isogeny class
Conductor	31824	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	196608	Modular degree for the optimal curve
Δ	12551221133568 = 28 · 310 · 132 · 173	Discriminant
Eigenvalues	2+ 3-  0 -2 -2 13+ 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1194015,-502183874]	[a1,a2,a3,a4,a6]
j	1008754689437602000/67254057	j-invariant
L	1.1554125958247	L(r)(E,1)/r!
Ω	0.14442657447792	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15912k1 127296cr1 10608g1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 31824b1

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	4	2	-10	4	0	4	-4	-10	4	10	4	14	-16	-8	0	-6	4

---

Quadratic twists for elliptic curve 31824b1

-4	8	-3
15912k1	127296cr1	10608g1

---

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