Elliptic curve isogeny class with Cremona label 169050ib (LMFDB label 169050.g)

• Label: 169050ib
• Number of curves: $4$
• Conductor: $169050$
• CM: no
• Rank: $1$

Elliptic curves in class 169050ib

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
169050.g4	169050ib1	\([1, 1, 0, 35500, 5970000]\)	\(2691419471/9891840\)	\(-18183829440000000\)	\([2]\)	\(1769472\)	\(1.8028\)	\(\Gamma_0(N)\)-optimal
169050.g3	169050ib2	\([1, 1, 0, -356500, 71434000]\)	\(2725812332209/373262400\)	\(686155439025000000\)	\([2, 2]\)	\(3538944\)	\(2.1494\)
169050.g1	169050ib3	\([1, 1, 0, -5501500, 4964329000]\)	\(10017490085065009/235066440\)	\(432114556243125000\)	\([2]\)	\(7077888\)	\(2.4960\)
169050.g2	169050ib4	\([1, 1, 0, -1483500, -623925000]\)	\(196416765680689/22365315000\)	\(41113389756796875000\)	\([2]\)	\(7077888\)	\(2.4960\)

Rank

The elliptic curves in class 169050ib have rank \(1\).

Complex multiplication

The elliptic curves in class 169050ib do not have complex multiplication.

Modular form 169050.2.a.ib

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.