Elliptic curve isogeny class with Cremona label 135450cu (LMFDB label 135450.dk)

• Label: 135450cu
• Number of curves: $2$
• Conductor: $135450$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 135450cu have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(43\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 135450cu do not have complex multiplication.

Modular form 135450.2.a.cu

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 135450cu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
135450.dk2	135450cu1	\([1, -1, 1, -2603855, -829221353]\)	\(6348375775125747/2706453299200\)	\(832361254502400000000\)	\([2]\)	\(5898240\)	\(2.7108\)	\(\Gamma_0(N)\)-optimal
135450.dk1	135450cu2	\([1, -1, 1, -19883855, 33557978647]\)	\(2826924016851247347/54574679290880\)	\(16784272070037360000000\)	\([2]\)	\(11796480\)	\(3.0574\)