Elliptic curve isogeny class 2500.3-d over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-2500.3-d
• Conductor: 2500.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 2500.3-d over \(\Q(\sqrt{-11}) \)

Isogeny class 2500.3-d contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
2500.3-d1	\( \bigl[a\) , \( 1\) , \( 1\) , \( -377 a + 251\) , \( -2207 a + 6069\bigr] \)
2500.3-d2	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 8 a - 5\) , \( -9 a - 32\bigr] \)
2500.3-d3	\( \bigl[a\) , \( 1\) , \( 1\) , \( -2 a + 1\) , \( -7 a + 19\bigr] \)
2500.3-d4	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -67 a + 20\) , \( 56 a + 238\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph