Elliptic curve isogeny class with Cremona label 64350cw (LMFDB label 64350.ef)

• Label: 64350cw
• Number of curves: $2$
• Conductor: $64350$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 64350cw have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 64350cw do not have complex multiplication.

Modular form 64350.2.a.cw

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 64350cw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
64350.ef1	64350cw1	\([1, -1, 1, -249605, 1385030397]\)	\(-4076600308125723/1961812478912000\)	\(-827639639541000000000\)	\([]\)	\(2612736\)	\(2.6929\)	\(\Gamma_0(N)\)-optimal
64350.ef2	64350cw2	\([1, -1, 1, 2246020, -37355388353]\)	\(4074304020054813/1962402098708480\)	\(-603530632951234560000000\)	\([]\)	\(7838208\)	\(3.2422\)