Elliptic curve isogeny class 3703.2-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-3703.2-a
• Conductor: 3703.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 3703.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 3703.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
3703.2-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -90 a + 351\) , \( 1496 a + 394\bigr] \)
3703.2-a2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 90 a + 261\) , \( -1496 a + 1890\bigr] \)
3703.2-a3	\( \bigl[1\) , \( -1\) , \( 1\) , \( 26\) , \( 36\bigr] \)
3703.2-a4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -9\) , \( 8\bigr] \)
3703.2-a5	\( \bigl[1\) , \( -1\) , \( 1\) , \( -4\) , \( -2\bigr] \)
3703.2-a6	\( \bigl[1\) , \( -1\) , \( 1\) , \( -124\) , \( 560\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 4 & 8 & 8 \\ 4 & 1 & 2 & 4 & 8 & 8 \\ 2 & 2 & 1 & 2 & 4 & 4 \\ 4 & 4 & 2 & 1 & 2 & 2 \\ 8 & 8 & 4 & 2 & 1 & 4 \\ 8 & 8 & 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph