Cremona's table of elliptic curves

212 = 2² · 53

Field	Data	Notes
Atkin-Lehner	2- 53+	Signs for the Atkin-Lehner involutions
Class	212b	Isogeny class
Conductor	212	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	21	Modular degree for the optimal curve
Δ	-719104 = -1 · 28 · 532	Discriminant
Eigenvalues	2-  2  2  0 -4 -2  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-12,-40]	[a1,a2,a3,a4,a6]
j	-810448/2809	j-invariant
L	1.7550063774399	L(r)(E,1)/r!
Ω	1.1700042516266	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	848d1 3392j2 1908b2 5300e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 212b1

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	2	0	-4	-2	2	2	-2	2	2	10	2	-4	-12	+	-12	10	-2	6	10	10	-6	-10	14

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Quadratic twists for elliptic curve 212b1

-4	8	-3	5	-7	-11	13	17	-19	-23	53
848d1	3392j2	1908b2	5300e2	10388g2	25652a2	35828g2	61268b2	76532f2	112148d2	11236b2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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