Elliptic curve isogeny class 22500.2-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-22500.2-c
• Conductor: 22500.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-2}) \)

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

Elliptic curves in class 22500.2-c over \(\Q(\sqrt{-2}) \)

Isogeny class 22500.2-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
22500.2-c1	\( \bigl[0\) , \( a\) , \( 0\) , \( -100 a - 134\) , \( 724 a + 275\bigr] \)
22500.2-c2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -26 a + 124\) , \( -407 a - 617\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph