Elliptic curve isogeny class with Cremona label 74529m (LMFDB label 74529.bg)

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

Rank

The elliptic curves in class 74529m 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.b
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 74529.2.a.m

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 74529m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
74529.bg1	74529m1	\([1, -1, 0, -163032, -25301431]\)	\(-56723625/13\)	\(-109830549012093\)	\([]\)	\(322560\)	\(1.6857\)	\(\Gamma_0(N)\)-optimal
74529.bg2	74529m2	\([1, -1, 0, 954903, 1047692582]\)	\(11397810375/62748517\)	\(-530131082446511601237\)	\([]\)	\(2257920\)	\(2.6587\)