Elliptic curve isogeny class 203.3-a over number field \(\Q(\sqrt{-13}) \)

• Base field: \(\Q(\sqrt{-13}) \)
• Label: 2.0.52.1-203.3-a
• Number of curves: 3
• Conductor: 203.3
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} + 13 \); class number \(2\).

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 203.3-a over \(\Q(\sqrt{-13}) \)

Isogeny class 203.3-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
203.3-a1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \)
203.3-a2	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a + 219\) , \( -311 a - 185\bigr] \)
203.3-a3	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a + 4\) , \( -10 a - 45\bigr] \)