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	312c	Isogeny class
Conductor	312	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	16848 = 24 · 34 · 13	Discriminant
Eigenvalues	2- 3-  2  0  0 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7,2]	[a1,a2,a3,a4,a6]
j	2725888/1053	j-invariant
L	1.7776867882324	L(r)(E,1)/r!
Ω	3.5553735764648	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	624c1 2496c1 936e1 7800a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 312c1

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
-	-	2	0	0	-	2	-4	0	6	0	-2	6	-12	-4	6	-8	-2	4	-12	-14	0	8	-18	-6

---

Quadratic twists for elliptic curve 312c1

-4	8	-3	5	-7	-11	13	17	-19
624c1	2496c1	936e1	7800a1	15288v1	37752i1	4056f1	90168v1	112632b1

---

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