| 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 |
| 1800.1-a1 |
1800.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 5^{2} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.482093190$ |
2.010387441 |
\( -\frac{162538}{135} a - \frac{404284}{135} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 24 a - 47\) , \( -151 a + 259\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(24a-47\right){x}-151a+259$ |
| 1800.1-a2 |
1800.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{11} \cdot 3^{9} \cdot 5^{4} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.482093190$ |
2.010387441 |
\( \frac{2025160829}{225} a + \frac{1345740931}{75} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 474 a - 857\) , \( -7513 a + 12949\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(474a-857\right){x}-7513a+12949$ |
| 1800.1-b1 |
1800.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.113657423$ |
2.375021220 |
\( -\frac{108}{5} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -3 a - 3\) , \( -36 a - 63\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a-3\right){x}-36a-63$ |
| 1800.1-b2 |
1800.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 5^{4} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.113657423$ |
2.375021220 |
\( \frac{3721734}{25} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -123 a - 213\) , \( -1086 a - 1881\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-123a-213\right){x}-1086a-1881$ |
| 1800.1-c1 |
1800.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 5^{2} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.655196615$ |
$4.112693932$ |
3.111482798 |
\( \frac{162538}{135} a - \frac{404284}{135} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -26 a - 47\) , \( -151 a - 261\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-26a-47\right){x}-151a-261$ |
| 1800.1-c2 |
1800.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{11} \cdot 3^{9} \cdot 5^{4} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.310393231$ |
$4.112693932$ |
3.111482798 |
\( -\frac{2025160829}{225} a + \frac{1345740931}{75} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -476 a - 857\) , \( -7513 a - 12951\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-476a-857\right){x}-7513a-12951$ |
| 1800.1-d1 |
1800.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{4} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.713428947$ |
1.566598933 |
\( \frac{126976}{25} a - \frac{206848}{25} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 20 a - 33\) , \( 55 a - 95\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(20a-33\right){x}+55a-95$ |
| 1800.1-d2 |
1800.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{2} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.426857894$ |
1.566598933 |
\( -\frac{457523264}{5} a + \frac{792477328}{5} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( a - 18\) , \( 7 a - 28\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-18\right){x}+7a-28$ |
| 1800.1-e1 |
1800.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{4} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.713428947$ |
1.566598933 |
\( -\frac{126976}{25} a - \frac{206848}{25} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -36 a + 63\) , \( 213 a - 369\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-36a+63\right){x}+213a-369$ |
| 1800.1-e2 |
1800.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{2} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.426857894$ |
1.566598933 |
\( \frac{457523264}{5} a + \frac{792477328}{5} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -a - 18\) , \( -7 a - 28\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-a-18\right){x}-7a-28$ |
| 1800.1-f1 |
1800.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{4} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.122188091$ |
$11.14610022$ |
3.145221174 |
\( -\frac{126976}{25} a - \frac{206848}{25} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -36 a + 63\) , \( -213 a + 369\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-36a+63\right){x}-213a+369$ |
| 1800.1-f2 |
1800.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{2} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.244376183$ |
$22.29220045$ |
3.145221174 |
\( \frac{457523264}{5} a + \frac{792477328}{5} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -a - 18\) , \( 7 a + 28\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-18\right){x}+7a+28$ |
| 1800.1-g1 |
1800.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{4} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.122188091$ |
$11.14610022$ |
3.145221174 |
\( \frac{126976}{25} a - \frac{206848}{25} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 20 a - 33\) , \( -55 a + 95\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(20a-33\right){x}-55a+95$ |
| 1800.1-g2 |
1800.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{2} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.244376183$ |
$22.29220045$ |
3.145221174 |
\( -\frac{457523264}{5} a + \frac{792477328}{5} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( a - 18\) , \( -7 a + 28\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(a-18\right){x}-7a+28$ |
| 1800.1-h1 |
1800.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 5^{2} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.482093190$ |
2.010387441 |
\( \frac{162538}{135} a - \frac{404284}{135} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -26 a - 47\) , \( 150 a + 259\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-26a-47\right){x}+150a+259$ |
| 1800.1-h2 |
1800.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{11} \cdot 3^{9} \cdot 5^{4} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.482093190$ |
2.010387441 |
\( -\frac{2025160829}{225} a + \frac{1345740931}{75} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -476 a - 857\) , \( 7512 a + 12949\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-476a-857\right){x}+7512a+12949$ |
| 1800.1-i1 |
1800.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.095459792$ |
$14.77018492$ |
3.256160336 |
\( -\frac{108}{5} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -4 a - 5\) , \( 31 a + 53\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-5\right){x}+31a+53$ |
| 1800.1-i2 |
1800.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 5^{4} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.190919584$ |
$14.77018492$ |
3.256160336 |
\( \frac{3721734}{25} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -124 a - 215\) , \( 871 a + 1511\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-124a-215\right){x}+871a+1511$ |
| 1800.1-j1 |
1800.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 5^{2} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.655196615$ |
$4.112693932$ |
3.111482798 |
\( -\frac{162538}{135} a - \frac{404284}{135} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 24 a - 47\) , \( 150 a - 261\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(24a-47\right){x}+150a-261$ |
| 1800.1-j2 |
1800.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{11} \cdot 3^{9} \cdot 5^{4} \) |
$2.01626$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.310393231$ |
$4.112693932$ |
3.111482798 |
\( \frac{2025160829}{225} a + \frac{1345740931}{75} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 474 a - 857\) , \( 7512 a - 12951\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(474a-857\right){x}+7512a-12951$ |
*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.
