Elliptic curve isogeny class 7744.20-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-7744.20-d
• Conductor: 7744.20
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 7744.20-d over \(\Q(\sqrt{-7}) \)

Isogeny class 7744.20-d contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
7744.20-d1	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 7820 a + 7820\) , \( 263579 a - 790739\bigr] \)
7744.20-d2	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 10 a + 10\) , \( 19 a - 59\bigr] \)
7744.20-d3	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 0\) , \( -a + 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph