Elliptic curve isogeny class with LMFDB label 83520.fi (Cremona label 83520dt)

• Label: 83520.fi
• Number of curves: $2$
• Conductor: $83520$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 83520.fi have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(29\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 83520.fi do not have complex multiplication.

Modular form 83520.2.a.fi

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 83520.fi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
83520.fi1	83520dt2	\([0, 0, 0, -6372, 243864]\)	\(-1419579648/453125\)	\(-9132912000000\)	\([]\)	\(110592\)	\(1.1998\)
83520.fi2	83520dt1	\([0, 0, 0, 588, -2984]\)	\(813189888/609725\)	\(-16857676800\)	\([]\)	\(36864\)	\(0.65053\)	\(\Gamma_0(N)\)-optimal