Cremona's table of elliptic curves

318 = 2 · 3 · 53

Field	Data	Notes
Atkin-Lehner	2- 3+ 53-	Signs for the Atkin-Lehner involutions
Class	318d	Isogeny class
Conductor	318	Conductor
∏ cp	22	Product of Tamagawa factors cp
deg	88	Modular degree for the optimal curve
Δ	-976896 = -1 · 211 · 32 · 53	Discriminant
Eigenvalues	2- 3+ -3 -4 -5 -2  5  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-12,45]	[a1,a2,a3,a4,a6]
Generators	[1:5:1]	Generators of the group modulo torsion
j	-192100033/976896	j-invariant
L	1.7453725128318	L(r)(E,1)/r!
Ω	2.412027248549	Real period
R	0.032891466822091	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	2544f1 10176g1 954c1 7950o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 318d1

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	-4	-5	-2	5	6	-7	-8	1	2	4	-1	-6	-	-3	-2	-10	0	-6	15	-10	-5	19

---

Quadratic twists for elliptic curve 318d1

-4	8	-3	5	-7	-11	13	17	-19	53
2544f1	10176g1	954c1	7950o1	15582ba1	38478b1	53742c1	91902bb1	114798k1	16854g1

---

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