Elliptic curve isogeny class with Cremona label 128700bp (LMFDB label 128700.bc)

• Label: 128700bp
• Number of curves: $2$
• Conductor: $128700$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 128700bp have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 128700bp do not have complex multiplication.

Modular form 128700.2.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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 128700bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
128700.bc1	128700bp1	\([0, 0, 0, -4260, 106225]\)	\(5864013824/50193\)	\(73181394000\)	\([2]\)	\(101376\)	\(0.90943\)	\(\Gamma_0(N)\)-optimal
128700.bc2	128700bp2	\([0, 0, 0, -1335, 249550]\)	\(-11279504/1146717\)	\(-26750614176000\)	\([2]\)	\(202752\)	\(1.2560\)