Properties

Base field \(\Q(\sqrt{105}) \)
Label 2.2.105.1-35.1-c
Conductor 35.1
Rank \( 1 \)

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Base field \(\Q(\sqrt{105}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 26 \); class number \(2\).

Elliptic curves in class 35.1-c over \(\Q(\sqrt{105}) \)

Isogeny class 35.1-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
35.1-c1 \( \bigl[0\) , \( a\) , \( a\) , \( 1445 a - 8134\) , \( -73135 a + 411269\bigr] \)
35.1-c2 \( \bigl[0\) , \( a\) , \( a\) , \( 15 a - 74\) , \( 55 a - 311\bigr] \)
35.1-c3 \( \bigl[0\) , \( a\) , \( a\) , \( -95 a + 546\) , \( -48 a + 271\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph