Elliptic curve isogeny class 441.1-j over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-441.1-j
• Conductor: 441.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{13}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).

Elliptic curves in class 441.1-j over \(\Q(\sqrt{13}) \)

Isogeny class 441.1-j contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
441.1-j1	\( \bigl[1\) , \( a\) , \( 1\) , \( 109 a - 31\) , \( 529 a + 1622\bigr] \)
441.1-j2	\( \bigl[1\) , \( a\) , \( 1\) , \( -31 a - 56\) , \( 103 a + 140\bigr] \)
441.1-j3	\( \bigl[1\) , \( a\) , \( 1\) , \( -171 a - 161\) , \( -1395 a - 1834\bigr] \)
441.1-j4	\( \bigl[1\) , \( a\) , \( 1\) , \( -31 a - 51\) , \( 121 a + 148\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph