Elliptic curve isogeny class with LMFDB label 224400.ik (Cremona label 224400cx)

• Label: 224400.ik
• Number of curves: $4$
• Conductor: $224400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 224400.ik have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(17\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 224400.ik do not have complex multiplication.

Modular form 224400.2.a.ik

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 224400.ik

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
224400.ik1	224400cx3	\([0, 1, 0, -561698808, 5123744882388]\)	\(306234591284035366263793/1727485056\)	\(110559043584000000\)	\([2]\)	\(33030144\)	\(3.3401\)
224400.ik2	224400cx2	\([0, 1, 0, -35106808, 80046706388]\)	\(74768347616680342513/5615307472896\)	\(359379678265344000000\)	\([2, 2]\)	\(16515072\)	\(2.9936\)
224400.ik3	224400cx4	\([0, 1, 0, -32802808, 91009138388]\)	\(-60992553706117024753/20624795251201152\)	\(-1319986896076873728000000\)	\([2]\)	\(33030144\)	\(3.3401\)
224400.ik4	224400cx1	\([0, 1, 0, -2338808, 1075826388]\)	\(22106889268753393/4969545596928\)	\(318050918203392000000\)	\([2]\)	\(8257536\)	\(2.6470\)	\(\Gamma_0(N)\)-optimal