Elliptic curve isogeny class with Cremona label 74529z (LMFDB label 74529.bf)

• Label: 74529z
• Number of curves: $4$
• Conductor: $74529$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 74529z have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 74529z do not have complex multiplication.

Modular form 74529.2.a.z

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 74529z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
74529.bf4	74529z1	\([1, -1, 0, 35712, -5542965]\)	\(12167/39\)	\(-16145090704777671\)	\([2]\)	\(387072\)	\(1.7932\)	\(\Gamma_0(N)\)-optimal
74529.bf3	74529z2	\([1, -1, 0, -336933, -64793520]\)	\(10218313/1521\)	\(629658537486329169\)	\([2, 2]\)	\(774144\)	\(2.1398\)
74529.bf2	74529z3	\([1, -1, 0, -1454868, 612004329]\)	\(822656953/85683\)	\(35470764278396543187\)	\([2]\)	\(1548288\)	\(2.4864\)
74529.bf1	74529z4	\([1, -1, 0, -5181318, -4538098629]\)	\(37159393753/1053\)	\(435917449028997117\)	\([2]\)	\(1548288\)	\(2.4864\)