Elliptic curve isogeny class with Cremona label 80325k (LMFDB label 80325.bu)

• Label: 80325k
• Number of curves: $3$
• Conductor: $80325$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 80325k have rank \(0\).

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 \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 80325.2.a.k

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 80325k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
80325.bu3	80325k1	\([0, 0, 1, -4428000, 3586406656]\)	\(22759502184972288000/5831\)	\(2459953125\)	\([]\)	\(715392\)	\(2.0844\)	\(\Gamma_0(N)\)-optimal
80325.bu2	80325k2	\([0, 0, 1, -4434750, 3574924031]\)	\(31363160518656000/198257271191\)	\(60973404200819578125\)	\([]\)	\(2146176\)	\(2.6337\)
80325.bu1	80325k3	\([0, 0, 1, -27587250, -53383698844]\)	\(838870874148864000/40675641638471\)	\(112586998270784722453125\)	\([]\)	\(6438528\)	\(3.1830\)