Elliptic curve isogeny class with Cremona label 13800u (LMFDB label 13800.z)

• Label: 13800u
• Number of curves: $2$
• Conductor: $13800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 13800u have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 13800u do not have complex multiplication.

Modular form 13800.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 13800u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13800.z2	13800u1	\([0, 1, 0, -72708, 7589088]\)	\(-10627137250000/110008287\)	\(-440033148000000\)	\([2]\)	\(64512\)	\(1.6275\)	\(\Gamma_0(N)\)-optimal
13800.z1	13800u2	\([0, 1, 0, -1166208, 484355088]\)	\(10963069081334500/1156923\)	\(18510768000000\)	\([2]\)	\(129024\)	\(1.9740\)