Elliptic curve isogeny class with Cremona label 65088bf (LMFDB label 65088.dm)

• Label: 65088bf
• Number of curves: $2$
• Conductor: $65088$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 65088bf have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(113\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 7 T + 13 T^{2}\)	1.13.ah
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 65088bf do not have complex multiplication.

Modular form 65088.2.a.bf

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 65088bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
65088.dm1	65088bf1	\([0, 0, 0, -1164, 13552]\)	\(912673/113\)	\(21594636288\)	\([2]\)	\(36864\)	\(0.71285\)	\(\Gamma_0(N)\)-optimal
65088.dm2	65088bf2	\([0, 0, 0, 1716, 70000]\)	\(2924207/12769\)	\(-2440193900544\)	\([2]\)	\(73728\)	\(1.0594\)