Cremona's table of elliptic curves

23712 = 2⁵ · 3 · 13 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 13- 19-	Signs for the Atkin-Lehner involutions
Class	23712o	Isogeny class
Conductor	23712	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	5888	Modular degree for the optimal curve
Δ	35141184 = 26 · 32 · 132 · 192	Discriminant
Eigenvalues	2- 3+ -2  0  0 13-  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-494,-4056]	[a1,a2,a3,a4,a6]
j	208738917568/549081	j-invariant
L	1.0126590280435	L(r)(E,1)/r!
Ω	1.0126590280436	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	23712q1 47424cw2 71136r1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 23712o1

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

---

Quadratic twists for elliptic curve 23712o1

-4	8	-3
23712q1	47424cw2	71136r1

---

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