Cremona's table of elliptic curves

507 = 3 · 13²

Field	Data	Notes
Atkin-Lehner	3+ 13+	Signs for the Atkin-Lehner involutions
Class	507c	Isogeny class
Conductor	507	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	-188245551 = -1 · 3 · 137	Discriminant
Eigenvalues	-1 3+ -2  4 -4 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,81,-564]	[a1,a2,a3,a4,a6]
Generators	[282:913:27]	Generators of the group modulo torsion
j	12167/39	j-invariant
L	1.1623161892614	L(r)(E,1)/r!
Ω	0.91712782597108	Real period
R	5.0693748738054	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8112bh1 32448be1 1521d1 12675w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 507c1

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	+	-2	4	-4	+	2	0	0	-10	-4	2	-6	-12	0	6	-12	-2	8	0	-2	8	-4	2	-10

---

Quadratic twists for elliptic curve 507c1

-4	8	-3	5	-7	-11	13
8112bh1	32448be1	1521d1	12675w1	24843s1	61347k1	39a4

---

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