Cremona's table of elliptic curves

67600 = 2⁴ · 5² · 13²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	67600u	Isogeny class
Conductor	67600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	368640	Modular degree for the optimal curve
Δ	16503906250000 = 24 · 514 · 132	Discriminant
Eigenvalues	2+ -3 5+ -3  5 13+ -3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-25675,-1571375]	[a1,a2,a3,a4,a6]
Generators	[640:15625:1]	Generators of the group modulo torsion
j	44302512384/390625	j-invariant
L	2.6686472621348	L(r)(E,1)/r!
Ω	0.37735750432536	Real period
R	1.7679834323188	Regulator
r	1	Rank of the group of rational points
S	0.99999999973815	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	33800k1 13520m1 67600t1	Quadratic twists by: -4 5 13

Hecke Eigenvalues for elliptic curve 67600u1

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
+	-3	+	-3	5	+	-3	-5	-3	-5	8	-9	-3	-1	12	-2	-5	-1	15	-1	-10	4	-12	1	7

---

Quadratic twists for elliptic curve 67600u1

-4	5	13
33800k1	13520m1	67600t1

---

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