Elliptic curve isogeny class with Cremona label 326700o (LMFDB label 326700.o)

• Label: 326700o
• Number of curves: $2$
• Conductor: $326700$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 326700o have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 326700o do not have complex multiplication.

Modular form 326700.2.a.o

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 Cremona numbering.

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

Isogeny graph

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

Elliptic curves in class 326700o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
326700.o2	326700o1	\([0, 0, 0, 9075, -166375]\)	\(6912/5\)	\(-59790183750000\)	\([]\)	\(933120\)	\(1.3318\)	\(\Gamma_0(N)\)-optimal
326700.o1	326700o2	\([0, 0, 0, -172425, -28117375]\)	\(-5267712/125\)	\(-13452791343750000\)	\([]\)	\(2799360\)	\(1.8812\)