Elliptic curve isogeny class with Cremona label 66240fd (LMFDB label 66240.df)

• Label: 66240fd
• Number of curves: $2$
• Conductor: $66240$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 66240fd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 66240fd do not have complex multiplication.

Modular form 66240.2.a.fd

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 66240fd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
66240.df1	66240fd1	\([0, 0, 0, -1668, 117592]\)	\(-687518464/7604375\)	\(-5676635520000\)	\([]\)	\(138240\)	\(1.1293\)	\(\Gamma_0(N)\)-optimal
66240.df2	66240fd2	\([0, 0, 0, 14892, -3035432]\)	\(489277573376/5615234375\)	\(-4191750000000000\)	\([]\)	\(414720\)	\(1.6786\)