Elliptic curve isogeny class with Cremona label 159120cr (LMFDB label 159120.q)

• Label: 159120cr
• Number of curves: $2$
• Conductor: $159120$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 159120cr have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(13\)	\(1 - T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 159120cr do not have complex multiplication.

Modular form 159120.2.a.cr

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 159120cr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
159120.q2	159120cr1	\([0, 0, 0, -48, -297]\)	\(-28311552/71825\)	\(-31028400\)	\([2]\)	\(30720\)	\(0.12533\)	\(\Gamma_0(N)\)-optimal
159120.q1	159120cr2	\([0, 0, 0, -1023, -12582]\)	\(17129586672/18785\)	\(129841920\)	\([2]\)	\(61440\)	\(0.47190\)