Elliptic curve isogeny class with LMFDB label 12600.bu (Cremona label 12600s)

• Label: 12600.bu
• Number of curves: $4$
• Conductor: $12600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 12600.bu have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	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 12600.bu do not have complex multiplication.

Modular form 12600.2.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 12600.bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12600.bu1	12600s3	\([0, 0, 0, -45588675, -115019523250]\)	\(898353183174324196/29899176238575\)	\(348743991646738800000000\)	\([2]\)	\(1474560\)	\(3.2903\)
12600.bu2	12600s2	\([0, 0, 0, -7001175, 4640314250]\)	\(13015144447800784/4341909875625\)	\(12661009197322500000000\)	\([2, 2]\)	\(737280\)	\(2.9437\)
12600.bu3	12600s1	\([0, 0, 0, -6298050, 6082423625]\)	\(151591373397612544/32558203125\)	\(5933732519531250000\)	\([2]\)	\(368640\)	\(2.5971\)	\(\Gamma_0(N)\)-optimal
12600.bu4	12600s4	\([0, 0, 0, 20336325, 32005151750]\)	\(79743193254623804/84085819746075\)	\(-980777001518218800000000\)	\([2]\)	\(1474560\)	\(3.2903\)