Cremona's table of elliptic curves

12600 = 2³ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7+	Signs for the Atkin-Lehner involutions
Class	12600bi	Isogeny class
Conductor	12600	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	1054885781250000 = 24 · 39 · 510 · 73	Discriminant
Eigenvalues	2- 3+ 5+ 7+ -2  2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-71550,-7198875]	[a1,a2,a3,a4,a6]
j	8232302592/214375	j-invariant
L	1.1694917634052	L(r)(E,1)/r!
Ω	0.29237294085131	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25200k1 100800i1 12600a1 2520d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12600bi1

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

---

Quadratic twists for elliptic curve 12600bi1

-4	8	-3	5	-7
25200k1	100800i1	12600a1	2520d1	88200er1

---

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