Elliptic curve isogeny class with LMFDB label 17424.cb (Cremona label 17424bl)

• Label: 17424.cb
• Number of curves: $2$
• Conductor: $17424$
• CM: \(\Q(\sqrt{-11}) \)
• Rank: $1$

Rank

The elliptic curves in class 17424.cb have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

Each elliptic curve in class 17424.cb has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-11}) \).

Modular form 17424.2.a.cb

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 17424.cb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
17424.cb1	17424bl2	\([0, 0, 0, -127776, -18037712]\)	\(-32768\)	\(-7040794078162944\)	\([]\)	\(95040\)	\(1.8183\)		\(-11\)
17424.cb2	17424bl1	\([0, 0, 0, -1056, 13552]\)	\(-32768\)	\(-3974344704\)	\([]\)	\(8640\)	\(0.61938\)	\(\Gamma_0(N)\)-optimal	\(-11\)