Elliptic curve isogeny class with LMFDB label 132300.er (Cremona label 132300ca)

• Label: 132300.er
• Number of curves: $2$
• Conductor: $132300$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 132300.er have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 132300.er do not have complex multiplication.

Modular form 132300.2.a.er

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 132300.er

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
132300.er1	132300ca2	\([0, 0, 0, -628425, 195638625]\)	\(-5267712/125\)	\(-651286481343750000\)	\([]\)	\(2239488\)	\(2.2045\)
132300.er2	132300ca1	\([0, 0, 0, 33075, 1157625]\)	\(6912/5\)	\(-2894606583750000\)	\([]\)	\(746496\)	\(1.6552\)	\(\Gamma_0(N)\)-optimal