| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 126976.1-a1 |
126976.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{38} \cdot 31^{3} \) |
$2.92166$ |
$(-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1$ |
$0.629755055$ |
1.454357002 |
\( -\frac{10618695}{29791} a - \frac{103188411}{59582} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -99 a + 128\) , \( -186 a - 611\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-99a+128\right){x}-186a-611$ |
| 126976.1-a2 |
126976.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{42} \cdot 31 \) |
$2.92166$ |
$(-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1$ |
$0.629755055$ |
1.454357002 |
\( \frac{44272737}{124} a + \frac{10648665}{248} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 389 a - 260\) , \( 2306 a + 129\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(389a-260\right){x}+2306a+129$ |
| 126976.1-b1 |
126976.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{30} \cdot 31 \) |
$2.92166$ |
$(-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.203329725$ |
$1.817290553$ |
3.413379681 |
\( -\frac{34992}{31} a + \frac{29160}{31} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 13 a\) , \( -6 a + 19\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+13a{x}-6a+19$ |
| 126976.1-c1 |
126976.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{46} \cdot 31^{5} \) |
$2.92166$ |
$(-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \) |
$1.752654364$ |
$0.230269866$ |
3.728144549 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -961 a + 353\) , \( 416 a - 5919\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-961a+353\right){x}+416a-5919$ |
| 126976.1-c2 |
126976.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{38} \cdot 31 \) |
$2.92166$ |
$(-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.350530872$ |
$1.151349331$ |
3.728144549 |
\( -\frac{24551}{62} a + \frac{45753}{31} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -a + 33\) , \( 32 a + 33\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-a+33\right){x}+32a+33$ |
| 126976.1-c3 |
126976.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{86} \cdot 31 \) |
$2.92166$ |
$(-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \) |
$8.763271822$ |
$0.046053973$ |
3.728144549 |
\( -\frac{936087656892551}{1040187392} a + \frac{51401239062153}{520093696} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 83199 a - 35167\) , \( 5257632 a + 3311393\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(83199a-35167\right){x}+5257632a+3311393$ |
| 126976.1-d1 |
126976.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{34} \cdot 31 \) |
$2.92166$ |
$(-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.222114189$ |
$1.405274489$ |
2.883346402 |
\( -\frac{20086}{31} a - \frac{49116}{31} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -21 a + 25\) , \( 12 a + 61\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-21a+25\right){x}+12a+61$ |
| 126976.1-e1 |
126976.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{30} \cdot 31 \) |
$2.92166$ |
$(-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.209461983$ |
$1.776075498$ |
3.436576292 |
\( -\frac{53240}{31} a - \frac{10648}{31} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 15 a - 15\) , \( 32 a - 15\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(15a-15\right){x}+32a-15$ |
| 126976.1-f1 |
126976.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{30} \cdot 31 \) |
$2.92166$ |
$(-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.333181105$ |
$1.776075498$ |
5.466396678 |
\( -\frac{53240}{31} a - \frac{10648}{31} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 15\) , \( -32 a + 15\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+15{x}-32a+15$ |
| 126976.1-g1 |
126976.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{34} \cdot 31 \) |
$2.92166$ |
$(-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.405274489$ |
3.245342418 |
\( -\frac{20086}{31} a - \frac{49116}{31} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4 a - 21\) , \( -12 a - 61\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-4a-21\right){x}-12a-61$ |
| 126976.1-h1 |
126976.1-h |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{46} \cdot 31^{5} \) |
$2.92166$ |
$(-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.230269866$ |
2.658927385 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 608 a - 961\) , \( -416 a + 5919\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(608a-961\right){x}-416a+5919$ |
| 126976.1-h2 |
126976.1-h |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{38} \cdot 31 \) |
$2.92166$ |
$(-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1.151349331$ |
2.658927385 |
\( -\frac{24551}{62} a + \frac{45753}{31} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -32 a - 1\) , \( -32 a - 33\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-32a-1\right){x}-32a-33$ |
| 126976.1-h3 |
126976.1-h |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{86} \cdot 31 \) |
$2.92166$ |
$(-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$25$ |
\( 2 \) |
$1$ |
$0.046053973$ |
2.658927385 |
\( -\frac{936087656892551}{1040187392} a + \frac{51401239062153}{520093696} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -48032 a + 83199\) , \( -5257632 a - 3311393\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-48032a+83199\right){x}-5257632a-3311393$ |
| 126976.1-i1 |
126976.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{30} \cdot 31 \) |
$2.92166$ |
$(-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.817290553$ |
4.196852761 |
\( -\frac{34992}{31} a + \frac{29160}{31} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -11 a + 12\) , \( 18 a - 31\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11a+12\right){x}+18a-31$ |
| 126976.1-j1 |
126976.1-j |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{38} \cdot 31^{3} \) |
$2.92166$ |
$(-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.414317070$ |
$0.629755055$ |
7.230779196 |
\( -\frac{10618695}{29791} a - \frac{103188411}{59582} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -99 a + 128\) , \( 186 a + 611\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-99a+128\right){x}+186a+611$ |
| 126976.1-j2 |
126976.1-j |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{42} \cdot 31 \) |
$2.92166$ |
$(-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$1.242951212$ |
$0.629755055$ |
7.230779196 |
\( \frac{44272737}{124} a + \frac{10648665}{248} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 389 a - 260\) , \( -2306 a - 129\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(389a-260\right){x}-2306a-129$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
