Elliptic curve isogeny class with LMFDB label 101640.bu (Cremona label 101640co)

• Label: 101640.bu
• Number of curves: $4$
• Conductor: $101640$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 101640.bu have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1 - T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	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 101640.bu do not have complex multiplication.

Modular form 101640.2.a.bu

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 101640.bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
101640.bu1	101640co4	\([0, 1, 0, -24516576, -45368464176]\)	\(898353183174324196/29899176238575\)	\(54239451705739433548800\)	\([2]\)	\(11059200\)	\(3.1352\)
101640.bu2	101640co2	\([0, 1, 0, -3765076, 1828747424]\)	\(13015144447800784/4341909875625\)	\(1969141299500057760000\)	\([2, 2]\)	\(5529600\)	\(2.7886\)
101640.bu3	101640co1	\([0, 1, 0, -3386951, 2397598674]\)	\(151591373397612544/32558203125\)	\(922861486181250000\)	\([2]\)	\(2764800\)	\(2.4420\)	\(\Gamma_0(N)\)-optimal
101640.bu4	101640co3	\([0, 1, 0, 10936424, 12625529024]\)	\(79743193254623804/84085819746075\)	\(-152538274729140606028800\)	\([2]\)	\(11059200\)	\(3.1352\)