Elliptic curve isogeny class 242.1-b over number field \(\Q(\sqrt{-13}) \)

• Base field: \(\Q(\sqrt{-13}) \)
• Label: 2.0.52.1-242.1-b
• Conductor: 242.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 242.1-b over \(\Q(\sqrt{-13}) \)

Isogeny class 242.1-b contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
242.1-b1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 16 a + 24\) , \( -22 a + 172\bigr] \)
242.1-b2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 40 a + 429\) , \( -999 a + 1227\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph