Elliptic curve isogeny class with LMFDB label 80325.bt (Cremona label 80325a)

• Label: 80325.bt
• Number of curves: $3$
• Conductor: $80325$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 80325.bt have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 80325.bt do not have complex multiplication.

Modular form 80325.2.a.bt

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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 80325.bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
80325.bt1	80325a2	\([0, 0, 1, -39852000, -96832979719]\)	\(22759502184972288000/5831\)	\(1793305828125\)	\([]\)	\(2146176\)	\(2.6337\)
80325.bt2	80325a3	\([0, 0, 1, -3065250, 1977174031]\)	\(838870874148864000/40675641638471\)	\(154440326846069578125\)	\([]\)	\(2146176\)	\(2.6337\)
80325.bt3	80325a1	\([0, 0, 1, -492750, -132404594]\)	\(31363160518656000/198257271191\)	\(83639786283703125\)	\([]\)	\(715392\)	\(2.0844\)	\(\Gamma_0(N)\)-optimal