Elliptic curve isogeny class with Cremona label 29744z (LMFDB label 29744.y)

• Label: 29744z
• Number of curves: $3$
• Conductor: $29744$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 29744z have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 29744z do not have complex multiplication.

Modular form 29744.2.a.z

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 29744z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
29744.y3	29744z1	\([0, 1, 0, -901, -25037]\)	\(-4096/11\)	\(-217476706304\)	\([]\)	\(17280\)	\(0.86289\)	\(\Gamma_0(N)\)-optimal
29744.y2	29744z2	\([0, 1, 0, -27941, 3246803]\)	\(-122023936/161051\)	\(-3184076456996864\)	\([]\)	\(86400\)	\(1.6676\)
29744.y1	29744z3	\([0, 1, 0, -21146181, 37420901363]\)	\(-52893159101157376/11\)	\(-217476706304\)	\([]\)	\(432000\)	\(2.4723\)