Elliptic curve isogeny class with Cremona label 161262z (LMFDB label 161262.b)

• Label: 161262z
• Number of curves: $2$
• Conductor: $161262$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 161262z have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(17\)	\(1\)
\(31\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 + 7 T + 13 T^{2}\)	1.13.h
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 161262z do not have complex multiplication.

Modular form 161262.2.a.z

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 161262z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
161262.b1	161262z1	\([1, -1, 0, -13926, 1359316]\)	\(-458314011/953312\)	\(-621287122820256\)	\([]\)	\(1209600\)	\(1.5277\)	\(\Gamma_0(N)\)-optimal
161262.b2	161262z2	\([1, -1, 0, 120459, -29325259]\)	\(406869021/1015808\)	\(-482610147801071616\)	\([]\)	\(3628800\)	\(2.0770\)