Cremona's table of elliptic curves

78 = 2 · 3 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13-	Signs for the Atkin-Lehner involutions
Class	78a	Isogeny class
Conductor	78	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	725251155408 = 24 · 320 · 13	Discriminant
Eigenvalues	2+ 3+  2  4 -4 13-  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2339,-15747]	[a1,a2,a3,a4,a6]
j	1416134368422073/725251155408	j-invariant
L	0.7252179630883	L(r)(E,1)/r!
Ω	0.7252179630883	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	624i4 2496j3 234d4 1950v3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 78a3

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	4	-4	-	2	-8	0	6	-4	-2	-10	4	8	-10	4	-2	-16	-8	2	8	12	14	10

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Quadratic twists for elliptic curve 78a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37
624i4	2496j3	234d4	1950v3	3822m4	9438u4	1014e3	22542n3	28158r3	41262g3	65598bl3	74958k3	106782j3

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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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