Elliptic curve isogeny class with Cremona label 22050cz (LMFDB label 22050.ed)

• Label: 22050cz
• Number of curves: $2$
• Conductor: $22050$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 22050cz have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 22050cz do not have complex multiplication.

Modular form 22050.2.a.cz

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 22050cz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
22050.ed2	22050cz1	\([1, -1, 1, 505, 10217]\)	\(179685/686\)	\(-54477369450\)	\([]\)	\(13824\)	\(0.74288\)	\(\Gamma_0(N)\)-optimal
22050.ed1	22050cz2	\([1, -1, 1, -25220, 1550287]\)	\(-30642435/56\)	\(-3241959373800\)	\([]\)	\(41472\)	\(1.2922\)