Elliptic curve isogeny class with LMFDB label 17424.ci (Cremona label 17424m)

• Label: 17424.ci
• Number of curves: $2$
• Conductor: $17424$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 17424.ci have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17424.ci do not have complex multiplication.

Modular form 17424.2.a.ci

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 17424.ci

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17424.ci1	17424m2	\([0, 0, 0, -1481403, -20936630]\)	\(102129622/59049\)	\(207875924760721840128\)	\([2]\)	\(1013760\)	\(2.5881\)
17424.ci2	17424m1	\([0, 0, 0, -1002243, 384911890]\)	\(63253004/243\)	\(427728240248398848\)	\([2]\)	\(506880\)	\(2.2415\)	\(\Gamma_0(N)\)-optimal