Elliptic curve isogeny class 238.2-d over number field \(\Q(\sqrt{-13}) \)

• Base field: \(\Q(\sqrt{-13}) \)
• Label: 2.0.52.1-238.2-d
• Conductor: 238.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 238.2-d over \(\Q(\sqrt{-13}) \)

Isogeny class 238.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
238.2-d1	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 84 a - 5965\) , \( -4964 a + 185381\bigr] \)
238.2-d2	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -76 a + 115\) , \( -900 a + 9509\bigr] \)
238.2-d3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 4 a - 45\) , \( 12 a - 27\bigr] \)
238.2-d4	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 4 a - 365\) , \( -116 a + 3237\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph