Cremona's table of elliptic curves

312 = 2³ · 3 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+	Signs for the Atkin-Lehner involutions
Class	312b	Isogeny class
Conductor	312	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	1872 = 24 · 32 · 13	Discriminant
Eigenvalues	2+ 3+  0 -4 -2 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3,0]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1]	Generators of the group modulo torsion
j	256000/117	j-invariant
L	1.4061524822049	L(r)(E,1)/r!
Ω	3.6898752966909	Real period
R	0.38108401209819	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	624d1 2496m1 936h1 7800w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 312b1

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

---

Quadratic twists for elliptic curve 312b1

-4	8	-3	5	-7	-11	13	17	-19
624d1	2496m1	936h1	7800w1	15288l1	37752s1	4056k1	90168k1	112632ba1

---

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