Elliptic curve isogeny class with LMFDB label 185900.bb (Cremona label 185900bd)

• Label: 185900.bb
• Number of curves: $4$
• Conductor: $185900$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 185900.bb have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 185900.bb do not have complex multiplication.

Modular form 185900.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 185900.bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
185900.bb1	185900bd4	\([0, -1, 0, -29998908, -63232089688]\)	\(154639330142416/33275\)	\(642448277900000000\)	\([2]\)	\(11197440\)	\(2.8016\)
185900.bb2	185900bd3	\([0, -1, 0, -1881533, -980221438]\)	\(610462990336/8857805\)	\(10688733223561250000\)	\([2]\)	\(5598720\)	\(2.4551\)
185900.bb3	185900bd2	\([0, -1, 0, -423908, -59889688]\)	\(436334416/171875\)	\(3318431187500000000\)	\([2]\)	\(3732480\)	\(2.2523\)
185900.bb4	185900bd1	\([0, -1, 0, -191533, 31666062]\)	\(643956736/15125\)	\(18251371531250000\)	\([2]\)	\(1866240\)	\(1.9058\)	\(\Gamma_0(N)\)-optimal