| 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 |
| 6.1-a1 |
6.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{18} \cdot 3^{8} \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.635076248$ |
4.207165779 |
\( -\frac{765055148}{9} a - \frac{513788887945}{648} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -792 a + 7624\) , \( 79552 a - 741312\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-792a+7624\right){x}+79552a-741312$ |
| 6.1-b1 |
6.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{18} \cdot 3^{8} \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.259884335$ |
$15.34926574$ |
5.132031674 |
\( \frac{765055148}{9} a - \frac{513788887945}{648} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 806 a + 7595\) , \( 91544 a + 854075\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(806a+7595\right){x}+91544a+854075$ |
| 6.1-c1 |
6.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{18} \cdot 3^{8} \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.635076248$ |
4.207165779 |
\( \frac{765055148}{9} a - \frac{513788887945}{648} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 792 a + 7624\) , \( -79552 a - 741312\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(792a+7624\right){x}-79552a-741312$ |
| 6.1-d1 |
6.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3 \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$24.55134397$ |
1.316090181 |
\( \frac{1639}{12} a + \frac{11115}{4} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -2031 a + 19199\) , \( 46506 a - 432995\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-2031a+19199\right){x}+46506a-432995$ |
| 6.1-e1 |
6.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3 \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.967071577$ |
$34.83450268$ |
3.611674542 |
\( -\frac{1639}{12} a + \frac{11115}{4} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 58 a - 304\) , \( -134 a + 1952\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(58a-304\right){x}-134a+1952$ |
| 6.1-f1 |
6.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{18} \cdot 3^{8} \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.259884335$ |
$15.34926574$ |
5.132031674 |
\( -\frac{765055148}{9} a - \frac{513788887945}{648} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -808 a + 7595\) , \( -91545 a + 854075\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-808a+7595\right){x}-91545a+854075$ |
| 6.1-g1 |
6.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3 \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$24.55134397$ |
1.316090181 |
\( -\frac{1639}{12} a + \frac{11115}{4} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 42 a - 333\) , \( 891 a - 8109\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(42a-333\right){x}+891a-8109$ |
| 6.1-h1 |
6.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3 \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.967071577$ |
$34.83450268$ |
3.611674542 |
\( \frac{1639}{12} a + \frac{11115}{4} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2047 a + 19140\) , \( -77084 a + 719158\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2047a+19140\right){x}-77084a+719158$ |
| 6.1-i1 |
6.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.461806566$ |
$34.83450268$ |
5.174058644 |
\( \frac{1639}{12} a + \frac{11115}{4} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -a + 31\) , \( -4 a + 18\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+31\right){x}-4a+18$ |
| 6.1-j1 |
6.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$1$ |
$24.55134397$ |
3.948270543 |
\( -\frac{1639}{12} a + \frac{11115}{4} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 39697 a - 370242\) , \( 10085230 a - 94068791\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(39697a-370242\right){x}+10085230a-94068791$ |
| 6.1-k1 |
6.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{6} \cdot 3^{8} \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \) |
$0.131604620$ |
$15.34926574$ |
3.465126529 |
\( -\frac{765055148}{9} a - \frac{513788887945}{648} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -27 a + 97\) , \( -49 a + 779\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-27a+97\right){x}-49a+779$ |
| 6.1-l1 |
6.1-l |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.461806566$ |
$34.83450268$ |
5.174058644 |
\( -\frac{1639}{12} a + \frac{11115}{4} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 39711 a - 370098\) , \( -9807302 a + 91477431\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(39711a-370098\right){x}-9807302a+91477431$ |
| 6.1-m1 |
6.1-m |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$1$ |
$24.55134397$ |
3.948270543 |
\( \frac{1639}{12} a + \frac{11115}{4} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 15 a + 203\) , \( 60 a + 662\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(15a+203\right){x}+60a+662$ |
| 6.1-n1 |
6.1-n |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{6} \cdot 3^{8} \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$1.635076248$ |
0.350597148 |
\( \frac{765055148}{9} a - \frac{513788887945}{648} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 10 a - 75\) , \( 99 a - 969\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-75\right){x}+99a-969$ |
| 6.1-o1 |
6.1-o |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{6} \cdot 3^{8} \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \) |
$0.131604620$ |
$15.34926574$ |
3.465126529 |
\( \frac{765055148}{9} a - \frac{513788887945}{648} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 26 a + 97\) , \( 49 a + 779\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(26a+97\right){x}+49a+779$ |
| 6.1-p1 |
6.1-p |
$1$ |
$1$ |
\(\Q(\sqrt{87}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{6} \cdot 3^{8} \) |
$2.60895$ |
$(2,a+1), (3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$1.635076248$ |
0.350597148 |
\( -\frac{765055148}{9} a - \frac{513788887945}{648} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -11 a - 75\) , \( -99 a - 969\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-11a-75\right){x}-99a-969$ |
*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.
