Elliptic curve isogeny class with Cremona label 132496bp (LMFDB label 132496.bz)

• Label: 132496bp
• Number of curves: $2$
• Conductor: $132496$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 132496bp have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 132496bp do not have complex multiplication.

Modular form 132496.2.a.bp

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 132496bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
132496.bz1	132496bp1	\([0, 0, 0, -14201915, 20604138282]\)	\(-56723625/13\)	\(-72601202540362682368\)	\([]\)	\(4515840\)	\(2.8025\)	\(\Gamma_0(N)\)-optimal
132496.bz2	132496bp2	\([0, 0, 0, 83182645, -852006965446]\)	\(11397810375/62748517\)	\(-350432137832645458518003712\)	\([]\)	\(31610880\)	\(3.7755\)