Elliptic curve isogeny class with LMFDB label 108300.bq (Cremona label 108300cd)

• Label: 108300.bq
• Number of curves: $4$
• Conductor: $108300$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 108300.bq have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(19\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 108300.bq do not have complex multiplication.

Modular form 108300.2.a.bq

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 108300.bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
108300.bq1	108300cd4	\([0, 1, 0, -333530908, 2343593055188]\)	\(21804712949838544/8680921875\)	\(1633606470006187500000000\)	\([2]\)	\(29859840\)	\(3.6100\)
108300.bq2	108300cd3	\([0, 1, 0, -24018533, 24726341688]\)	\(130287139815424/52926616125\)	\(622494820987357781250000\)	\([2]\)	\(14929920\)	\(3.2634\)
108300.bq3	108300cd2	\([0, 1, 0, -11879908, -11769494812]\)	\(985329269584/252434475\)	\(47504009084589900000000\)	\([2]\)	\(9953280\)	\(3.0607\)
108300.bq4	108300cd1	\([0, 1, 0, -11022533, -14087836812]\)	\(12592337649664/1315845\)	\(15476271821111250000\)	\([2]\)	\(4976640\)	\(2.7141\)	\(\Gamma_0(N)\)-optimal