Elliptic curve isogeny class with Cremona label 86240bb (LMFDB label 86240.bp)

• Label: 86240bb
• Number of curves: $2$
• Conductor: $86240$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 86240bb have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 86240bb do not have complex multiplication.

Modular form 86240.2.a.bb

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 86240bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
86240.bp2	86240bb1	\([0, -1, 0, 894, 18656]\)	\(3595640768/9150625\)	\(-200874520000\)	\([2]\)	\(73728\)	\(0.85260\)	\(\Gamma_0(N)\)-optimal
86240.bp1	86240bb2	\([0, -1, 0, -7576, 215160]\)	\(273865201784/47265625\)	\(8300600000000\)	\([2]\)	\(147456\)	\(1.1992\)