Elliptic curve isogeny class with LMFDB label 22050.eh (Cremona label 22050da)

• Label: 22050.eh
• Number of curves: $4$
• Conductor: $22050$
• CM: no
• Rank: $1$

Elliptic curves in class 22050.eh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
22050.eh1	22050da3	\([1, -1, 1, -514730, 124681897]\)	\(416832723/56000\)	\(2026224608625000000\)	\([2]\)	\(331776\)	\(2.2402\)
22050.eh2	22050da1	\([1, -1, 1, -128855, -17748853]\)	\(4767078987/6860\)	\(340483559062500\)	\([2]\)	\(110592\)	\(1.6909\)	\(\Gamma_0(N)\)-optimal
22050.eh3	22050da2	\([1, -1, 1, -92105, -28112353]\)	\(-1740992427/5882450\)	\(-291964651896093750\)	\([2]\)	\(221184\)	\(2.0375\)
22050.eh4	22050da4	\([1, -1, 1, 808270, 659173897]\)	\(1613964717/6125000\)	\(-221618316568359375000\)	\([2]\)	\(663552\)	\(2.5868\)

Rank

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

Complex multiplication

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

Modular form 22050.2.a.eh

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.