Elliptic curve isogeny class with LMFDB label 65340.w (Cremona label 65340bh)

• Label: 65340.w
• Number of curves: $2$
• Conductor: $65340$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 65340.w have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 65340.w do not have complex multiplication.

Modular form 65340.2.a.w

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 65340.w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
65340.w1	65340bh2	\([0, 0, 0, -62073, 6073353]\)	\(-5267712/125\)	\(-627653432934000\)	\([]\)	\(349920\)	\(1.6257\)
65340.w2	65340bh1	\([0, 0, 0, 3267, 35937]\)	\(6912/5\)	\(-2789570813040\)	\([]\)	\(116640\)	\(1.0764\)	\(\Gamma_0(N)\)-optimal