Elliptic curve isogeny class with LMFDB label 51744.bb (Cremona label 51744v)

• Label: 51744.bb
• Number of curves: $4$
• Conductor: $51744$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 51744.bb have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 51744.bb do not have complex multiplication.

Modular form 51744.2.a.bb

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 51744.bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51744.bb1	51744v4	\([0, -1, 0, -2535472, -1553102648]\)	\(29925549856274696/4851\)	\(292206233088\)	\([2]\)	\(491520\)	\(2.0440\)
51744.bb2	51744v3	\([0, -1, 0, -182737, -16291295]\)	\(1400416996672/570715299\)	\(275022168932560896\)	\([2]\)	\(491520\)	\(2.0440\)
51744.bb3	51744v1	\([0, -1, 0, -158482, -24222680]\)	\(58465284603328/23532201\)	\(177186554588736\)	\([2, 2]\)	\(245760\)	\(1.6974\)	\(\Gamma_0(N)\)-optimal
51744.bb4	51744v2	\([0, -1, 0, -134472, -31838652]\)	\(-4464412682696/4706920449\)	\(-283527415759053312\)	\([2]\)	\(491520\)	\(2.0440\)