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	31824k	Isogeny class
Conductor	31824	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	57344	Modular degree for the optimal curve
Δ	173719323648 = 210 · 310 · 132 · 17	Discriminant
Eigenvalues	2+ 3-  2 -4  6 13+ 17- -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3819,-88598]	[a1,a2,a3,a4,a6]
Generators	[-39:32:1]	Generators of the group modulo torsion
j	8251733668/232713	j-invariant
L	5.8858411187226	L(r)(E,1)/r!
Ω	0.6083597786976	Real period
R	2.4187336691304	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	15912e1 127296dw1 10608f1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 31824k1

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	-4	6	+	-	-8	6	-8	0	-2	0	-4	8	6	12	-8	16	-8	-12	-10	16	10	-12

---

Quadratic twists for elliptic curve 31824k1

-4	8	-3
15912e1	127296dw1	10608f1

---

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