| 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 |
| 100.1-a1 |
100.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{4} \) |
$2.71039$ |
$(-a+5), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$4$ |
\( 2 \) |
$1$ |
$2.224996764$ |
1.855775586 |
\( \frac{92296192}{5} a - \frac{2213166336}{25} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 118 a - 561\) , \( 1769 a - 8486\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(118a-561\right){x}+1769a-8486$ |
| 100.1-b1 |
100.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{4} \) |
$2.71039$ |
$(-a+5), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$4$ |
\( 2 \) |
$1$ |
$2.224996764$ |
1.855775586 |
\( -\frac{92296192}{5} a - \frac{2213166336}{25} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -118 a - 561\) , \( -1769 a - 8486\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-118a-561\right){x}-1769a-8486$ |
| 100.1-c1 |
100.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{4} \) |
$2.71039$ |
$(-a+5), (5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.384792628$ |
$17.02000671$ |
5.462387985 |
\( -\frac{92296192}{5} a - \frac{2213166336}{25} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -118 a - 561\) , \( 1769 a + 8486\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-118a-561\right){x}+1769a+8486$ |
| 100.1-d1 |
100.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$2.71039$ |
$(-a+5), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \) |
$1.787624877$ |
$6.044583093$ |
4.506182947 |
\( \frac{6912}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 240 a + 1151\) , \( 55224 a + 264845\bigr] \) |
${y}^2={x}^{3}+\left(240a+1151\right){x}+55224a+264845$ |
| 100.1-e1 |
100.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{4} \) |
$2.71039$ |
$(-a+5), (5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.384792628$ |
$17.02000671$ |
5.462387985 |
\( \frac{92296192}{5} a - \frac{2213166336}{25} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 118 a - 561\) , \( -1769 a + 8486\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(118a-561\right){x}-1769a+8486$ |
| 100.1-f1 |
100.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$2.71039$ |
$(-a+5), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$10.34365470$ |
1.617600825 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 2178 a - 10441\) , \( -178033 a + 853818\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(2178a-10441\right){x}-178033a+853818$ |
| 100.1-f2 |
100.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$2.71039$ |
$(-a+5), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$10.34365470$ |
1.617600825 |
\( \frac{21296}{25} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -222 a + 1069\) , \( 3327 a - 15954\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-222a+1069\right){x}+3327a-15954$ |
| 100.1-f3 |
100.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$2.71039$ |
$(-a+5), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$20.68730941$ |
1.617600825 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-{x}$ |
| 100.1-f4 |
100.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$2.71039$ |
$(-a+5), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$20.68730941$ |
1.617600825 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-41{x}+116$ |
| 100.1-g1 |
100.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{4} \) |
$2.71039$ |
$(-a+5), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.493902753$ |
$6.143509620$ |
3.796167114 |
\( -\frac{38112512}{25} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4240 a - 20334\) , \( 330712 a - 1586039\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(4240a-20334\right){x}+330712a-1586039$ |
| 100.1-h1 |
100.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$2.71039$ |
$(-a+5), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \) |
$1.787624877$ |
$6.044583093$ |
4.506182947 |
\( \frac{6912}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 240 a + 1151\) , \( -55224 a - 264845\bigr] \) |
${y}^2={x}^{3}+\left(240a+1151\right){x}-55224a-264845$ |
| 100.1-i1 |
100.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{4} \) |
$2.71039$ |
$(-a+5), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.493902753$ |
$6.143509620$ |
3.796167114 |
\( -\frac{38112512}{25} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4240 a - 20334\) , \( -330712 a - 1586039\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-4240a-20334\right){x}-330712a-1586039$ |
| 100.1-j1 |
100.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$2.71039$ |
$(-a+5), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 3 \) |
$0.800486153$ |
$8.729749266$ |
4.371323333 |
\( -\frac{33554432}{5} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( -3\) , \( 5 a - 6\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}-3{x}+5a-6$ |
| 100.1-k1 |
100.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$2.71039$ |
$(-a+5), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 3 \) |
$0.800486153$ |
$8.729749266$ |
4.371323333 |
\( -\frac{33554432}{5} \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( -3\) , \( -6 a - 6\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}-3{x}-6a-6$ |
| 100.1-l1 |
100.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$2.71039$ |
$(-a+5), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3 \) |
$1$ |
$1.772687765$ |
2.495008916 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 2182 a - 10441\) , \( 186753 a - 895614\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(2182a-10441\right){x}+186753a-895614$ |
| 100.1-l2 |
100.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$2.71039$ |
$(-a+5), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$9$ |
\( 2 \cdot 3 \) |
$1$ |
$15.95418988$ |
2.495008916 |
\( \frac{21296}{25} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -218 a + 1069\) , \( -4207 a + 20198\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-218a+1069\right){x}-4207a+20198$ |
| 100.1-l3 |
100.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$2.71039$ |
$(-a+5), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$9$ |
\( 3 \) |
$1$ |
$31.90837977$ |
2.495008916 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}$ |
| 100.1-l4 |
100.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$2.71039$ |
$(-a+5), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$3.545375530$ |
2.495008916 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-41{x}-116$ |
*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.
