Elliptic curve isogeny class 71148.2-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-71148.2-e
• Conductor: 71148.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-3}) \)

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

Elliptic curves in class 71148.2-e over \(\Q(\sqrt{-3}) \)

Isogeny class 71148.2-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
71148.2-e1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -97 a + 97\) , \( 1337\bigr] \)
71148.2-e2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -3507 a + 3507\) , \( 6507\bigr] \)
71148.2-e3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2517 a + 2517\) , \( 48285\bigr] \)
71148.2-e4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -40247 a + 40247\) , \( 3104415\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph