Cremona's table of elliptic curves

2812 = 2² · 19 · 37

Field	Data	Notes
Atkin-Lehner	2- 19+ 37+	Signs for the Atkin-Lehner involutions
Class	2812a	Isogeny class
Conductor	2812	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	1689894300928 = 28 · 194 · 373	Discriminant
Eigenvalues	2- -1  2 -3  5  2  0 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3277,37193]	[a1,a2,a3,a4,a6]
j	15207071653888/6601149613	j-invariant
L	1.5150188027268	L(r)(E,1)/r!
Ω	0.75750940136342	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11248m1 44992t1 25308d1 70300a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2812a1

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	-3	5	2	0	+	2	-2	4	+	-5	-2	5	-7	12	8	0	-1	15	8	15	-12	16

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Quadratic twists for elliptic curve 2812a1

-4	8	-3	5	-19	37
11248m1	44992t1	25308d1	70300a1	53428d1	104044c1

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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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