Elliptic curve isogeny class with Cremona label 18450o (LMFDB label 18450.h)

• Label: 18450o
• Number of curves: $2$
• Conductor: $18450$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 18450o have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(41\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 18450o do not have complex multiplication.

Modular form 18450.2.a.o

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 18450o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
18450.h1	18450o1	\([1, -1, 0, -14967, -697059]\)	\(32553430057/212544\)	\(2421009000000\)	\([2]\)	\(49152\)	\(1.2122\)	\(\Gamma_0(N)\)-optimal
18450.h2	18450o2	\([1, -1, 0, -5967, -1534059]\)	\(-2062933417/88232328\)	\(-1005021361125000\)	\([2]\)	\(98304\)	\(1.5587\)