Elliptic curve isogeny class 5625.3-d over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-5625.3-d
• Conductor: 5625.3
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-11}) \)

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

Elliptic curves in class 5625.3-d over \(\Q(\sqrt{-11}) \)

Isogeny class 5625.3-d contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
5625.3-d1	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 592 a + 2344\) , \( 28760 a - 44213\bigr] \)
5625.3-d2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 192 a + 97\) , \( 1860 a - 1140\bigr] \)
5625.3-d3	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -8 a + 22\) , \( -15 a - 15\bigr] \)
5625.3-d4	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 17 a + 19\) , \( -40 a + 112\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)

Isogeny graph