Elliptic curve isogeny class with Cremona label 108900df (LMFDB label 108900.br)

• Label: 108900df
• Number of curves: $2$
• Conductor: $108900$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 108900df have rank \(1\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 108900df do not have complex multiplication.

Modular form 108900.2.a.df

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 108900df

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
108900.br1	108900df1	\([0, 0, 0, -27588000, -45973571875]\)	\(57537462272/10673289\)	\(430756589605626281250000\)	\([2]\)	\(11059200\)	\(3.2532\)	\(\Gamma_0(N)\)-optimal
108900.br2	108900df2	\([0, 0, 0, 54767625, -267921981250]\)	\(28134667888/64304361\)	\(-41523511249256404500000000\)	\([2]\)	\(22118400\)	\(3.5998\)