Elliptic curve isogeny class with LMFDB label 74529.bi (Cremona label 74529i)

• Label: 74529.bi
• Number of curves: $2$
• Conductor: $74529$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 74529.bi have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 74529.2.a.bi

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 74529.bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
74529.bi1	74529i1	\([1, -1, 0, -38817, -2321656]\)	\(421875/91\)	\(1395254752264737\)	\([2]\)	\(258048\)	\(1.6200\)	\(\Gamma_0(N)\)-optimal
74529.bi2	74529i2	\([1, -1, 0, 85398, -14221453]\)	\(4492125/8281\)	\(-126968182456091067\)	\([2]\)	\(516096\)	\(1.9666\)