Elliptic curve isogeny class with Cremona label 99099i (LMFDB label 99099.bv)

• Label: 99099i
• Number of curves: $2$
• Conductor: $99099$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 99099i have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(7\)	\(1 - T\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 99099i do not have complex multiplication.

Modular form 99099.2.a.i

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 99099i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
99099.bv1	99099i1	\([1, -1, 0, -567, -3976]\)	\(421875/91\)	\(4352725377\)	\([2]\)	\(46080\)	\(0.56355\)	\(\Gamma_0(N)\)-optimal
99099.bv2	99099i2	\([1, -1, 0, 1248, -25393]\)	\(4492125/8281\)	\(-396098009307\)	\([2]\)	\(92160\)	\(0.91012\)