| 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 |
| 75.1-a1 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{32} \cdot 5^{2} \) |
$2.53598$ |
$(a+4), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.547989231$ |
2.113713401 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -9574 a - 41356\) , \( 2099208 a + 9072429\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9574a-41356\right){x}+2099208a+9072429$ |
| 75.1-a2 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$2.53598$ |
$(a+4), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$10.19195692$ |
2.113713401 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -4 a + 4\) , \( -472 a - 2021\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+4\right){x}-472a-2021$ |
| 75.1-a3 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{16} \) |
$2.53598$ |
$(a+4), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.547989231$ |
2.113713401 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 3041 a + 13164\) , \( 107608 a + 465082\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3041a+13164\right){x}+107608a+465082$ |
| 75.1-a4 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$2.53598$ |
$(a+4), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$10.19195692$ |
2.113713401 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -874 a - 3756\) , \( 14008 a + 60559\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-874a-3756\right){x}+14008a+60559$ |
| 75.1-a5 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$2.53598$ |
$(a+4), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$10.19195692$ |
2.113713401 |
\( \frac{13997521}{225} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 439 a - 2316\) , \( 11311 a - 60156\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(439a-2316\right){x}+11311a-60156$ |
| 75.1-a6 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$2.53598$ |
$(a+4), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$10.19195692$ |
2.113713401 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -11749 a - 50756\) , \( 1518008 a + 6560584\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11749a-50756\right){x}+1518008a+6560584$ |
| 75.1-a7 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$2.53598$ |
$(a+4), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$2.547989231$ |
2.113713401 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -6964 a - 30076\) , \( -696072 a - 3008283\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6964a-30076\right){x}-696072a-3008283$ |
| 75.1-a8 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$2.53598$ |
$(a+4), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$10.19195692$ |
2.113713401 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -187924 a - 812156\) , \( 97324808 a + 420620839\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-187924a-812156\right){x}+97324808a+420620839$ |
| 75.1-b1 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{32} \cdot 5^{2} \) |
$2.53598$ |
$(a+4), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$39.45005330$ |
$0.490422220$ |
2.006209393 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$ |
| 75.1-b2 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$2.53598$ |
$(a+4), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.465628331$ |
$31.38702211$ |
2.006209393 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$ |
| 75.1-b3 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{16} \) |
$2.53598$ |
$(a+4), (5)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$19.72502665$ |
$1.961688882$ |
2.006209393 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$ |
| 75.1-b4 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$2.53598$ |
$(a+4), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$9.862513326$ |
$7.846755528$ |
2.006209393 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$ |
| 75.1-b5 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$2.53598$ |
$(a+4), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$4.931256663$ |
$31.38702211$ |
2.006209393 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$ |
| 75.1-b6 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$2.53598$ |
$(a+4), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$19.72502665$ |
$1.961688882$ |
2.006209393 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$ |
| 75.1-b7 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$2.53598$ |
$(a+4), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.465628331$ |
$31.38702211$ |
2.006209393 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$ |
| 75.1-b8 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$2.53598$ |
$(a+4), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$39.45005330$ |
$0.490422220$ |
2.006209393 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$ |
*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.
