Cremona's table of elliptic curves

12558 = 2 · 3 · 7 · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 13- 23+	Signs for the Atkin-Lehner involutions
Class	12558n	Isogeny class
Conductor	12558	Conductor
∏ cp	768	Product of Tamagawa factors cp
Δ	451521457781599296 = 26 · 34 · 78 · 134 · 232	Discriminant
Eigenvalues	2- 3+  2 7-  0 13-  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-9738467,-11701269439]	[a1,a2,a3,a4,a6]
j	102139918202985795140993713/451521457781599296	j-invariant
L	4.1022134836621	L(r)(E,1)/r!
Ω	0.085462780909627	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	100464bs2 37674k2 87906bn2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12558n2

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

---

Quadratic twists for elliptic curve 12558n2

-4	-3	-7
100464bs2	37674k2	87906bn2

---

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