Elliptic curve isogeny class 6875.3-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-6875.3-b
• Conductor: 6875.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 6875.3-b over \(\Q(\sqrt{-11}) \)

Isogeny class 6875.3-b contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
6875.3-b1	\( \bigl[0\) , \( 1\) , \( 1\) , \( -195508\) , \( -33338481\bigr] \)
6875.3-b2	\( \bigl[0\) , \( 1\) , \( 1\) , \( -258\) , \( -2981\bigr] \)
6875.3-b3	\( \bigl[0\) , \( 1\) , \( 1\) , \( -8\) , \( 19\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph