Elliptic curve isogeny class with LMFDB label 144400.bb (Cremona label 144400o)

• Label: 144400.bb
• Number of curves: $4$
• Conductor: $144400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 144400.bb have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 144400.bb do not have complex multiplication.

Modular form 144400.2.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.

\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 144400.bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
144400.bb1	144400o4	\([0, -1, 0, -18125208, -29695651088]\)	\(-349938025/8\)	\(-15054681920000000000\)	\([]\)	\(4860000\)	\(2.7933\)
144400.bb2	144400o3	\([0, -1, 0, -75208, -93651088]\)	\(-25/2\)	\(-3763670480000000000\)	\([]\)	\(1620000\)	\(2.2440\)
144400.bb3	144400o1	\([0, -1, 0, -17448, 1075312]\)	\(-121945/32\)	\(-154159942860800\)	\([]\)	\(324000\)	\(1.4393\)	\(\Gamma_0(N)\)-optimal
144400.bb4	144400o2	\([0, -1, 0, 126952, -7935248]\)	\(46969655/32768\)	\(-157859781489459200\)	\([]\)	\(972000\)	\(1.9886\)