Cremona's table of elliptic curves

650 = 2 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 5- 13+	Signs for the Atkin-Lehner involutions
Class	650k	Isogeny class
Conductor	650	Conductor
∏ cp	42	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	-13520000 = -1 · 27 · 54 · 132	Discriminant
Eigenvalues	2- -1 5- -4  1 13+ -7 -3	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,12,181]	[a1,a2,a3,a4,a6]
Generators	[25:117:1]	Generators of the group modulo torsion
j	304175/21632	j-invariant
L	2.4329160965982	L(r)(E,1)/r!
Ω	1.7063199853737	Real period
R	0.033948247822839	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5200be1 20800bv1 5850v1 650d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650k1

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
-	-1	-	-4	1	+	-7	-3	0	-4	6	-8	-5	-4	12	-10	4	8	-9	-8	13	8	3	-11	-10

---

Quadratic twists for elliptic curve 650k1

-4	8	-3	5	-7	-11	13
5200be1	20800bv1	5850v1	650d1	31850cm1	78650bk1	8450j1

---

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