| 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 |
| 2.1-a1 |
2.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{10} \) |
$1.62209$ |
$(a-8)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$16.03897468$ |
2.101496335 |
\( \frac{117913}{1024} a + \frac{835841}{1024} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 927211 a - 7540096\) , \( 24963534685 a - 203007676600\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(927211a-7540096\right){x}+24963534685a-203007676600$ |
| 2.2-a1 |
2.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
2.2 |
\( 2 \) |
\( - 2^{10} \) |
$1.62209$ |
$(a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$16.03897468$ |
2.101496335 |
\( -\frac{117913}{1024} a + \frac{476877}{512} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -927212 a - 6612884\) , \( -24963534685 a - 178044141915\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-927212a-6612884\right){x}-24963534685a-178044141915$ |
| 4.1-a1 |
4.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{15} \) |
$1.92900$ |
$(a-8), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$15.75112776$ |
3.611617411 |
\( -\frac{497763387}{16384} a + \frac{1677336471}{8192} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 55429669 a - 450763423\) , \( 619296480248 a - 5036223490617\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(55429669a-450763423\right){x}+619296480248a-5036223490617$ |
| 4.1-a2 |
4.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{9} \) |
$1.92900$ |
$(a-8), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$15.75112776$ |
3.611617411 |
\( -\frac{15541279083}{128} a + \frac{126384283773}{128} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -671 a - 4786\) , \( -89588 a - 638957\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-671a-4786\right){x}-89588a-638957$ |
| 4.1-a3 |
4.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{15} \) |
$1.92900$ |
$(a-8), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$15.75112776$ |
3.611617411 |
\( \frac{497763387}{16384} a + \frac{2856909555}{16384} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -55429669 a - 395333754\) , \( -619296480248 a - 4416927010369\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-55429669a-395333754\right){x}-619296480248a-4416927010369$ |
| 4.1-a4 |
4.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{9} \) |
$1.92900$ |
$(a-8), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$15.75112776$ |
3.611617411 |
\( \frac{15541279083}{128} a + \frac{55421502345}{64} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 671 a - 5457\) , \( 89588 a - 728545\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(671a-5457\right){x}+89588a-728545$ |
| 4.1-b1 |
4.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{16} \) |
$1.92900$ |
$(a-8), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$7$ |
7B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$1.429464645$ |
2.622125591 |
\( -\frac{149093490420875}{16384} a - \frac{1063359914919875}{16384} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -1213 a + 9886\) , \( 38514 a - 313249\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1213a+9886\right){x}+38514a-313249$ |
| 4.1-b2 |
4.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{16} \) |
$1.92900$ |
$(a-8), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$7$ |
7B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$1.429464645$ |
2.622125591 |
\( \frac{149093490420875}{16384} a - \frac{606226702670375}{8192} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 1214 a + 8673\) , \( -37302 a - 266061\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1214a+8673\right){x}-37302a-266061$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{16} \) |
$2.29398$ |
$(a-8), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$6.957774151$ |
3.646551521 |
\( -\frac{1893425}{256} a - \frac{6529979}{128} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -19296 a - 137602\) , \( -4162450 a - 29687249\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-19296a-137602\right){x}-4162450a-29687249$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$2.29398$ |
$(a-8), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.491787192$ |
$19.69915118$ |
2.538672965 |
\( \frac{371}{4} a + \frac{1585}{2} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -4190268 a + 34076069\) , \( -45057515215 a + 366415317890\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-4190268a+34076069\right){x}-45057515215a+366415317890$ |
| 8.1-c1 |
8.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$2.29398$ |
$(a-8), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$5.765473608$ |
3.777087345 |
\( -\frac{890109}{1024} a - \frac{2584575}{512} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -1577 a - 11129\) , \( -103928 a - 740984\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1577a-11129\right){x}-103928a-740984$ |
| 8.1-d1 |
8.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{13} \) |
$2.29398$ |
$(a-8), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 5 \) |
$1$ |
$12.01814735$ |
3.936675056 |
\( -\frac{1553657467801775}{32} a - \frac{5540473628757477}{16} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -2400189 a - 17118546\) , \( 5572954097 a + 39747249122\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2400189a-17118546\right){x}+5572954097a+39747249122$ |
| 8.1-e1 |
8.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{10} \) |
$2.29398$ |
$(a-8), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$6.629808368$ |
2.605999124 |
\( -\frac{105922969}{4} a + \frac{430694349}{2} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 12 a - 50\) , \( 94 a - 641\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(12a-50\right){x}+94a-641$ |
| 8.2-a1 |
8.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{16} \) |
$2.29398$ |
$(a-8), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$6.957774151$ |
3.646551521 |
\( \frac{1893425}{256} a - \frac{14953383}{256} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 19294 a - 156898\) , \( 4162449 a - 33849699\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(19294a-156898\right){x}+4162449a-33849699$ |
| 8.2-b1 |
8.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$2.29398$ |
$(a-8), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.491787192$ |
$19.69915118$ |
2.538672965 |
\( -\frac{371}{4} a + \frac{3541}{4} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 4190268 a + 29885801\) , \( 45057515215 a + 321357802675\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4190268a+29885801\right){x}+45057515215a+321357802675$ |
| 8.2-c1 |
8.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{18} \) |
$2.29398$ |
$(a-8), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$5.765473608$ |
3.777087345 |
\( \frac{890109}{1024} a - \frac{6059259}{1024} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 1577 a - 12707\) , \( 105505 a - 857619\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1577a-12707\right){x}+105505a-857619$ |
| 8.2-d1 |
8.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{13} \) |
$2.29398$ |
$(a-8), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 5 \) |
$1$ |
$12.01814735$ |
3.936675056 |
\( \frac{1553657467801775}{32} a - \frac{12634604725316729}{32} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 2400219 a - 19518706\) , \( -5590072643 a + 45459415022\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(2400219a-19518706\right){x}-5590072643a+45459415022$ |
| 8.2-e1 |
8.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{10} \) |
$2.29398$ |
$(a-8), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$6.629808368$ |
2.605999124 |
\( \frac{105922969}{4} a + \frac{755465729}{4} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -14 a - 38\) , \( -95 a - 547\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-14a-38\right){x}-95a-547$ |
| 9.1-a1 |
9.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{4} \) |
$2.36253$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$21.23480674$ |
2.782276886 |
\( -\frac{943177}{9} a + 851754 \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 15377 a - 124972\) , \( -2805341 a + 22813645\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(15377a-124972\right){x}-2805341a+22813645$ |
| 9.1-b1 |
9.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{4} \) |
$2.36253$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$21.23480674$ |
2.782276886 |
\( \frac{943177}{9} a + \frac{6722609}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -15378 a - 109595\) , \( 2805341 a + 20008304\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15378a-109595\right){x}+2805341a+20008304$ |
| 13.1-a1 |
13.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
13.1 |
\( 13 \) |
\( - 13^{2} \) |
$2.59002$ |
$(38a+271)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1.105170559$ |
$32.96377612$ |
9.546590498 |
\( \frac{1499441417}{169} a - \frac{12193048847}{169} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -57 a - 348\) , \( -658 a - 4567\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-57a-348\right){x}-658a-4567$ |
| 13.1-b1 |
13.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
13.1 |
\( 13 \) |
\( - 13^{2} \) |
$2.59002$ |
$(38a+271)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.104937269$ |
$46.39973246$ |
1.275931228 |
\( \frac{1325161}{169} a + \frac{9235793}{169} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 70272 a - 571337\) , \( -42788527 a + 347963812\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(70272a-571337\right){x}-42788527a+347963812$ |
| 13.2-a1 |
13.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
13.2 |
\( 13 \) |
\( - 13^{2} \) |
$2.59002$ |
$(38a-309)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1.105170559$ |
$32.96377612$ |
9.546590498 |
\( -\frac{1499441417}{169} a - \frac{10693607430}{169} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 55 a - 404\) , \( 657 a - 5225\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(55a-404\right){x}+657a-5225$ |
| 13.2-b1 |
13.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
13.2 |
\( 13 \) |
\( - 13^{2} \) |
$2.59002$ |
$(38a-309)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.104937269$ |
$46.39973246$ |
1.275931228 |
\( -\frac{1325161}{169} a + \frac{10560954}{169} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -70273 a - 501064\) , \( 42788527 a + 305175285\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-70273a-501064\right){x}+42788527a+305175285$ |
| 14.1-a1 |
14.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{10} \cdot 7^{13} \) |
$2.63845$ |
$(a+7), (-8a-57)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 13 \) |
$0.151765466$ |
$4.910233882$ |
2.538636523 |
\( -\frac{13893306186535537599}{99214346656768} a - \frac{49714917902480716181}{49607173328384} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 16684570467 a - 135681742760\) , \( -3973875075855982 a + 32316222752933831\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(16684570467a-135681742760\right){x}-3973875075855982a+32316222752933831$ |
| 14.1-b1 |
14.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{3} \) |
$2.63845$ |
$(a+7), (-8a-57)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1.209001874$ |
$2.568145533$ |
2.440899457 |
\( -\frac{2459822491383}{21952} a - \frac{8771918366717}{10976} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -1638239 a - 11684179\) , \( -3167264915 a - 22589467875\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1638239a-11684179\right){x}-3167264915a-22589467875$ |
| 14.1-b2 |
14.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7 \) |
$2.63845$ |
$(a+7), (-8a-57)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$3.627005624$ |
$23.11330979$ |
2.440899457 |
\( \frac{61569}{28} a - \frac{258773}{14} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -16184 a - 115409\) , \( -6236862 a - 44482342\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-16184a-115409\right){x}-6236862a-44482342$ |
| 14.2-a1 |
14.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{10} \cdot 7 \) |
$2.63845$ |
$(a+7), (8a-65)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$29.12073000$ |
4.769406134 |
\( -\frac{2439949}{7168} a + \frac{9814353}{3584} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( a + 18\) , \( -2 a - 9\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+18\right){x}-2a-9$ |
| 14.2-a2 |
14.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{5} \cdot 7^{2} \) |
$2.63845$ |
$(a+7), (8a-65)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$29.12073000$ |
4.769406134 |
\( \frac{17198499}{1568} a + \frac{61696241}{784} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -1337 a - 9515\) , \( 69836 a + 498064\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1337a-9515\right){x}+69836a+498064$ |
| 14.2-b1 |
14.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$2.63845$ |
$(a+7), (8a-65)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$8.120621682$ |
4.255996918 |
\( -\frac{402069}{784} a - \frac{1076815}{392} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( a + 19\) , \( 2 a + 6\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+19\right){x}+2a+6$ |
| 14.2-c1 |
14.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{11} \cdot 7^{3} \) |
$2.63845$ |
$(a+7), (8a-65)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.397938658$ |
$13.03290588$ |
2.038593709 |
\( \frac{406619231783}{702464} a + \frac{1450358933773}{351232} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -15886990 a - 113308678\) , \( 95170985461 a + 678775529469\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-15886990a-113308678\right){x}+95170985461a+678775529469$ |
| 14.2-d1 |
14.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{2} \) |
$2.63845$ |
$(a+7), (8a-65)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$7.569962060$ |
1.983698814 |
\( -\frac{170239625}{196} a + \frac{692192125}{98} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -409968 a - 2923947\) , \( -1326197897 a - 9458667206\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-409968a-2923947\right){x}-1326197897a-9458667206$ |
| 14.3-a1 |
14.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2^{5} \cdot 7^{2} \) |
$2.63845$ |
$(a-8), (-8a-57)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$29.12073000$ |
4.769406134 |
\( -\frac{17198499}{1568} a + \frac{140590981}{1568} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 1337 a - 10852\) , \( -69836 a + 567900\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(1337a-10852\right){x}-69836a+567900$ |
| 14.3-a2 |
14.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2^{10} \cdot 7 \) |
$2.63845$ |
$(a-8), (-8a-57)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$29.12073000$ |
4.769406134 |
\( \frac{2439949}{7168} a + \frac{17188757}{7168} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( a + 18\) , \( 2 a + 7\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+18\right){x}+2a+7$ |
| 14.3-b1 |
14.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$2.63845$ |
$(a-8), (-8a-57)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$8.120621682$ |
4.255996918 |
\( \frac{402069}{784} a - \frac{2555699}{784} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( a + 18\) , \( -2 a - 11\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+18\right){x}-2a-11$ |
| 14.3-c1 |
14.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2^{11} \cdot 7^{3} \) |
$2.63845$ |
$(a-8), (-8a-57)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.397938658$ |
$13.03290588$ |
2.038593709 |
\( -\frac{406619231783}{702464} a + \frac{3307337099329}{702464} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 15886990 a - 129195668\) , \( -95170985461 a + 773946514930\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(15886990a-129195668\right){x}-95170985461a+773946514930$ |
| 14.3-d1 |
14.3-d |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{2} \) |
$2.63845$ |
$(a-8), (-8a-57)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$7.569962060$ |
1.983698814 |
\( \frac{170239625}{196} a + \frac{1214144625}{196} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 409999 a - 3333886\) , \( 1323273951 a - 10761086089\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(409999a-3333886\right){x}+1323273951a-10761086089$ |
| 14.4-a1 |
14.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.4 |
\( 2 \cdot 7 \) |
\( 2^{10} \cdot 7^{13} \) |
$2.63845$ |
$(a-8), (8a-65)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 13 \) |
$0.151765466$ |
$4.910233882$ |
2.538636523 |
\( \frac{13893306186535537599}{99214346656768} a - \frac{113323141991496969961}{99214346656768} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -16684570469 a - 118997172292\) , \( 3973875075855981 a + 28342347677077850\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-16684570469a-118997172292\right){x}+3973875075855981a+28342347677077850$ |
| 14.4-b1 |
14.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.4 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7 \) |
$2.63845$ |
$(a-8), (8a-65)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$3.627005624$ |
$23.11330979$ |
2.440899457 |
\( -\frac{61569}{28} a - \frac{455977}{28} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 16213 a - 131623\) , \( 6105239 a - 49648039\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(16213a-131623\right){x}+6105239a-49648039$ |
| 14.4-b2 |
14.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
14.4 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{3} \) |
$2.63845$ |
$(a-8), (8a-65)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1.209001874$ |
$2.568145533$ |
2.440899457 |
\( \frac{2459822491383}{21952} a - \frac{20003659224817}{21952} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 1638268 a - 13322448\) , \( 3153942467 a - 25648391610\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1638268a-13322448\right){x}+3153942467a-25648391610$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$2.72801$ |
$(a-8), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$9.482065365$ |
1.863572268 |
\( -5428048 a + 44135200 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 136 a - 1084\) , \( -2056 a + 16700\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(136a-1084\right){x}-2056a+16700$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$2.72801$ |
$(a-8), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$9.482065365$ |
1.863572268 |
\( 5428048 a + 38707152 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -136 a - 948\) , \( 2056 a + 14644\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-136a-948\right){x}+2056a+14644$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$2.72801$ |
$(a-8), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$26.57255954$ |
1.740826256 |
\( -2000 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -234184347 a - 1670242262\) , \( 7358337486852 a + 52480904758384\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-234184347a-1670242262\right){x}+7358337486852a+52480904758384$ |
| 16.2-a1 |
16.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{9} \) |
$2.72801$ |
$(a-8), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.424745688$ |
$23.90599346$ |
5.321668306 |
\( \frac{1039}{2} a - \frac{6681}{2} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 22593518 a - 183734082\) , \( -180205879737 a + 1465464626579\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(22593518a-183734082\right){x}-180205879737a+1465464626579$ |
| 16.3-a1 |
16.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{9} \) |
$2.72801$ |
$(a-8), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.424745688$ |
$23.90599346$ |
5.321668306 |
\( -\frac{1039}{2} a - 2821 \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -22593489 a - 161140562\) , \( 180022145655 a + 1283948323582\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-22593489a-161140562\right){x}+180022145655a+1283948323582$ |
| 16.4-a1 |
16.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( - 2^{22} \) |
$2.72801$ |
$(a-8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.428651822$ |
$14.67927226$ |
1.648888280 |
\( \frac{117913}{1024} a + \frac{835841}{1024} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( 23 a - 165\) , \( -3069 a + 24961\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(23a-165\right){x}-3069a+24961$ |
| 16.5-a1 |
16.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( - 2^{22} \) |
$2.72801$ |
$(a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.428651822$ |
$14.67927226$ |
1.648888280 |
\( -\frac{117913}{1024} a + \frac{476877}{512} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -23 a - 142\) , \( 3068 a + 21892\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-23a-142\right){x}+3068a+21892$ |
| 18.1-a1 |
18.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{8} \) |
$2.80954$ |
$(a-8), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.478388431$ |
0.424413337 |
\( -\frac{168952051}{54} a + \frac{4122071569}{162} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 72700197 a + 518510074\) , \( -424780239267 a - 3029604352891\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(72700197a+518510074\right){x}-424780239267a-3029604352891$ |
| 18.1-a2 |
18.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{4} \) |
$2.80954$ |
$(a-8), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$25.91355372$ |
0.424413337 |
\( -\frac{13225}{36} a + \frac{182291}{36} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -20155368 a - 143751486\) , \( -55733526825 a - 397500918975\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-20155368a-143751486\right){x}-55733526825a-397500918975$ |
| 18.1-a3 |
18.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{233}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{4} \cdot 3^{2} \) |
$2.80954$ |
$(a-8), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$25.91355372$ |
0.424413337 |
\( \frac{234625}{48} a + \frac{1685369}{48} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -21486 a + 174739\) , \( 11463829 a - 93225825\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-21486a+174739\right){x}+11463829a-93225825$ |
*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.
