Elliptic curve isogeny class with Cremona label 9900u (LMFDB label 9900.bc)

• Label: 9900u
• Number of curves: $4$
• Conductor: $9900$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 9900u have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9900u do not have complex multiplication.

Modular form 9900.2.a.u

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 9900u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9900.bc3	9900u1	\([0, 0, 0, -9300, -451375]\)	\(-488095744/200475\)	\(-36536568750000\)	\([2]\)	\(27648\)	\(1.3108\)	\(\Gamma_0(N)\)-optimal
9900.bc2	9900u2	\([0, 0, 0, -161175, -24903250]\)	\(158792223184/16335\)	\(47632860000000\)	\([2]\)	\(55296\)	\(1.6573\)
9900.bc4	9900u3	\([0, 0, 0, 71700, 4935125]\)	\(223673040896/187171875\)	\(-34112074218750000\)	\([2]\)	\(82944\)	\(1.8601\)
9900.bc1	9900u4	\([0, 0, 0, -350175, 43325750]\)	\(1628514404944/664335375\)	\(1937201953500000000\)	\([2]\)	\(165888\)	\(2.2066\)