Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-30.1-c
Conductor 30.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{15}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 15 \); class number \(2\).

Elliptic curves in class 30.1-c over \(\Q(\sqrt{15}) \)

Isogeny class 30.1-c contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
30.1-c1 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -432 a - 1675\) , \( -32562 a - 126115\bigr] \)
30.1-c2 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 48 a + 185\) , \( 1182 a + 4577\bigr] \)
30.1-c3 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -14512 a - 56235\) , \( -288562 a - 1117635\bigr] \)
30.1-c4 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2192 a - 8495\) , \( -99842 a - 386695\bigr] \)
30.1-c5 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -592 a - 2295\) , \( 12638 a + 48945\bigr] \)
30.1-c6 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -10672 a - 41355\) , \( -1204018 a - 4663203\bigr] \)
30.1-c7 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -9232 a - 35775\) , \( 929342 a + 3599337\bigr] \)
30.1-c8 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -170672 a - 661355\) , \( -75956018 a - 294179203\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph