Elliptic curve isogeny class with Cremona label 162624cm (LMFDB label 162624.t)

• Label: 162624cm
• Number of curves: $4$
• Conductor: $162624$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 162624cm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 162624cm do not have complex multiplication.

Modular form 162624.2.a.cm

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 162624cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162624.t4	162624cm1	\([0, -1, 0, -4991169, -1418198175]\)	\(29609739866953/15259926528\)	\(7086772243626775805952\)	\([2]\)	\(11059200\)	\(2.8848\)	\(\Gamma_0(N)\)-optimal
162624.t2	162624cm2	\([0, -1, 0, -44640449, 113794679649]\)	\(21184262604460873/216872764416\)	\(100716598106934051078144\)	\([2, 2]\)	\(22118400\)	\(3.2314\)
162624.t1	162624cm3	\([0, -1, 0, -712483009, 7320216607585]\)	\(86129359107301290313/9166294368\)	\(4256864565164362432512\)	\([2]\)	\(44236800\)	\(3.5780\)
162624.t3	162624cm4	\([0, -1, 0, -11186369, 280362543969]\)	\(-333345918055753/72923718045024\)	\(-33866072683593272515362816\)	\([2]\)	\(44236800\)	\(3.5780\)