| 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 |
| 5.1-a1 |
5.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 2^{12} \cdot 5^{6} \) |
$2.29894$ |
$(5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$17.62602985$ |
2.048984351 |
\( -\frac{88629248}{15625} a + \frac{819265536}{15625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1948 a - 16757\) , \( 98812 a + 850013\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-1948a-16757\right){x}+98812a+850013$ |
| 5.1-a2 |
5.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 2^{12} \cdot 5^{2} \) |
$2.29894$ |
$(5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$9$ |
\( 2 \) |
$1$ |
$1.958447761$ |
2.048984351 |
\( -\frac{1474198135201792}{25} a + \frac{12681531941535744}{25} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -56868 a - 489197\) , \( -21663436 a - 186355923\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-56868a-489197\right){x}-21663436a-186355923$ |
| 5.1-b1 |
5.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 5^{6} \) |
$2.29894$ |
$(5,a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$2.566136054$ |
$17.62602985$ |
3.505315078 |
\( -\frac{88629248}{15625} a + \frac{819265536}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -487 a - 4189\) , \( 12595 a + 108346\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-487a-4189\right){x}+12595a+108346$ |
| 5.1-b2 |
5.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$2.29894$ |
$(5,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$7.698408163$ |
$1.958447761$ |
3.505315078 |
\( -\frac{1474198135201792}{25} a + \frac{12681531941535744}{25} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -14217 a - 122299\) , \( -2700821 a - 23233341\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-14217a-122299\right){x}-2700821a-23233341$ |
| 5.2-a1 |
5.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( 2^{12} \cdot 5^{6} \) |
$2.29894$ |
$(5,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$17.62602985$ |
2.048984351 |
\( \frac{88629248}{15625} a + \frac{819265536}{15625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1948 a - 16757\) , \( -98812 a + 850013\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(1948a-16757\right){x}-98812a+850013$ |
| 5.2-a2 |
5.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( 2^{12} \cdot 5^{2} \) |
$2.29894$ |
$(5,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$9$ |
\( 2 \) |
$1$ |
$1.958447761$ |
2.048984351 |
\( \frac{1474198135201792}{25} a + \frac{12681531941535744}{25} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 56868 a - 489197\) , \( 21663436 a - 186355923\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(56868a-489197\right){x}+21663436a-186355923$ |
| 5.2-b1 |
5.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( 5^{6} \) |
$2.29894$ |
$(5,a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$2.566136054$ |
$17.62602985$ |
3.505315078 |
\( \frac{88629248}{15625} a + \frac{819265536}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 487 a - 4189\) , \( -12595 a + 108346\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(487a-4189\right){x}-12595a+108346$ |
| 5.2-b2 |
5.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( 5^{2} \) |
$2.29894$ |
$(5,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$7.698408163$ |
$1.958447761$ |
3.505315078 |
\( \frac{1474198135201792}{25} a + \frac{12681531941535744}{25} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 14217 a - 122299\) , \( 2700821 a - 23233341\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(14217a-122299\right){x}+2700821a-23233341$ |
| 13.1-a1 |
13.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
13.1 |
\( 13 \) |
\( 2^{12} \cdot 13^{2} \) |
$2.91924$ |
$(13,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.320774595$ |
$31.17677453$ |
2.325119529 |
\( -\frac{622592}{169} a + \frac{9535488}{169} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 1\) , \( -13 a - 125\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+1\right){x}-13a-125$ |
| 13.1-b1 |
13.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
13.1 |
\( 13 \) |
\( 13^{2} \) |
$2.91924$ |
$(13,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$31.17677453$ |
3.624226423 |
\( -\frac{622592}{169} a + \frac{9535488}{169} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 19\) , \( -2 a - 16\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+19{x}-2a-16$ |
| 13.2-a1 |
13.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
13.2 |
\( 13 \) |
\( 2^{12} \cdot 13^{2} \) |
$2.91924$ |
$(13,a+10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.320774595$ |
$31.17677453$ |
2.325119529 |
\( \frac{622592}{169} a + \frac{9535488}{169} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a + 1\) , \( 13 a - 125\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+1\right){x}+13a-125$ |
| 13.2-b1 |
13.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
13.2 |
\( 13 \) |
\( 13^{2} \) |
$2.91924$ |
$(13,a+10)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$31.17677453$ |
3.624226423 |
\( \frac{622592}{169} a + \frac{9535488}{169} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 19\) , \( a - 16\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+19{x}+a-16$ |
| 20.1-a1 |
20.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{10} \) |
$3.25119$ |
$(2,a), (5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$10.63342345$ |
6.180551843 |
\( -\frac{89803888095665152}{9765625} a + \frac{772522348321035264}{9765625} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -517884 a - 4454982\) , \( 539598822 a + 4641804604\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-517884a-4454982\right){x}+539598822a+4641804604$ |
| 20.1-b1 |
20.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{10} \) |
$3.25119$ |
$(2,a), (5,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.638237332$ |
$10.63342345$ |
4.733590708 |
\( -\frac{89803888095665152}{9765625} a + \frac{772522348321035264}{9765625} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 38229 a - 328858\) , \( -11920555 a + 102544473\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(38229a-328858\right){x}-11920555a+102544473$ |
| 20.2-a1 |
20.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{10} \) |
$3.25119$ |
$(2,a), (5,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$10.63342345$ |
6.180551843 |
\( \frac{89803888095665152}{9765625} a + \frac{772522348321035264}{9765625} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 517884 a - 4454982\) , \( -539598822 a + 4641804604\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(517884a-4454982\right){x}-539598822a+4641804604$ |
| 20.2-b1 |
20.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{10} \) |
$3.25119$ |
$(2,a), (5,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.638237332$ |
$10.63342345$ |
4.733590708 |
\( \frac{89803888095665152}{9765625} a + \frac{772522348321035264}{9765625} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -38229 a - 328858\) , \( 11920555 a + 102544473\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-38229a-328858\right){x}+11920555a+102544473$ |
| 25.2-a1 |
25.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$3.43771$ |
$(5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$1$ |
$18.28958640$ |
2.126121233 |
\( 4096 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -769402 a - 6618627\) , \( -816779767 a - 7026205211\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-769402a-6618627\right){x}-816779767a-7026205211$ |
| 25.2-a2 |
25.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$3.43771$ |
$(5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$1$ |
$18.28958640$ |
2.126121233 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -162343962 a - 1396535547\) , \( 3302885938577 a + 28412499163597\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-162343962a-1396535547\right){x}+3302885938577a+28412499163597$ |
| 25.2-b1 |
25.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$3.43771$ |
$(5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$1$ |
$18.28958640$ |
2.126121233 |
\( 4096 \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 2 a + 2\) , \( 11 a - 111\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+2\right){x}+11a-111$ |
| 25.2-b2 |
25.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$3.43771$ |
$(5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$1$ |
$18.28958640$ |
2.126121233 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 562 a - 4828\) , \( -19547 a + 168183\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(562a-4828\right){x}-19547a+168183$ |
| 25.3-a1 |
25.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$3.43771$ |
$(5,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$1$ |
$18.28958640$ |
2.126121233 |
\( 4096 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 769402 a - 6618627\) , \( 816779767 a - 7026205211\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(769402a-6618627\right){x}+816779767a-7026205211$ |
| 25.3-a2 |
25.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$3.43771$ |
$(5,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$1$ |
$18.28958640$ |
2.126121233 |
\( 38477541376 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 162343962 a - 1396535547\) , \( -3302885938577 a + 28412499163597\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(162343962a-1396535547\right){x}-3302885938577a+28412499163597$ |
| 25.3-b1 |
25.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$3.43771$ |
$(5,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$1$ |
$18.28958640$ |
2.126121233 |
\( 4096 \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -2 a + 2\) , \( -11 a - 111\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+2\right){x}-11a-111$ |
| 25.3-b2 |
25.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$3.43771$ |
$(5,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$1$ |
$18.28958640$ |
2.126121233 |
\( 38477541376 \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -562 a - 4828\) , \( 19547 a + 168183\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-562a-4828\right){x}+19547a+168183$ |
| 28.1-a1 |
28.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{20} \cdot 7^{3} \) |
$3.53650$ |
$(2,a), (-a-9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 3^{2} \) |
$1$ |
$1.023536779$ |
4.818841216 |
\( \frac{120411322964}{343} a - \frac{1035824133852}{343} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 3356 a - 28845\) , \( 300769 a - 2587290\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(3356a-28845\right){x}+300769a-2587290$ |
| 28.1-a2 |
28.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{20} \cdot 7 \) |
$3.53650$ |
$(2,a), (-a-9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$9.211831012$ |
4.818841216 |
\( \frac{1156}{7} a + \frac{1692}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 36 a - 285\) , \( 441 a - 3770\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(36a-285\right){x}+441a-3770$ |
| 28.1-b1 |
28.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$3.53650$ |
$(2,a), (-a-9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.023536779$ |
0.178475600 |
\( \frac{120411322964}{343} a - \frac{1035824133852}{343} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 826 a - 7103\) , \( 46613 a - 400951\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(826a-7103\right){x}+46613a-400951$ |
| 28.1-b2 |
28.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$3.53650$ |
$(2,a), (-a-9)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$9.211831012$ |
0.178475600 |
\( \frac{1156}{7} a + \frac{1692}{7} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -4 a + 37\) , \( 107 a - 891\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+37\right){x}+107a-891$ |
| 28.2-a1 |
28.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{20} \cdot 7^{3} \) |
$3.53650$ |
$(2,a), (a-9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 3^{2} \) |
$1$ |
$1.023536779$ |
4.818841216 |
\( -\frac{120411322964}{343} a - \frac{1035824133852}{343} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -3356 a - 28845\) , \( -300769 a - 2587290\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-3356a-28845\right){x}-300769a-2587290$ |
| 28.2-a2 |
28.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{20} \cdot 7 \) |
$3.53650$ |
$(2,a), (a-9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$9.211831012$ |
4.818841216 |
\( -\frac{1156}{7} a + \frac{1692}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -36 a - 285\) , \( -441 a - 3770\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-36a-285\right){x}-441a-3770$ |
| 28.2-b1 |
28.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$3.53650$ |
$(2,a), (a-9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.023536779$ |
0.178475600 |
\( -\frac{120411322964}{343} a - \frac{1035824133852}{343} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -826 a - 7103\) , \( -46613 a - 400951\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-826a-7103\right){x}-46613a-400951$ |
| 28.2-b2 |
28.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$3.53650$ |
$(2,a), (a-9)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$9.211831012$ |
0.178475600 |
\( -\frac{1156}{7} a + \frac{1692}{7} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 4 a + 37\) , \( -107 a - 891\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+37\right){x}-107a-891$ |
| 32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$3.65655$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$27.50074327$ |
0.399612058 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 32.1-a2 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$3.65655$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 2 \) |
$1$ |
$13.75037163$ |
0.399612058 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+4{x}$ |
| 32.1-a3 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$3.65655$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$13.75037163$ |
0.399612058 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \) |
${y}^2={x}^{3}-11{x}-14$ |
| 32.1-a4 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$3.65655$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$55.00148654$ |
0.399612058 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \) |
${y}^2={x}^{3}-11{x}+14$ |
| 32.1-b1 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$3.65655$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$6.782710350$ |
$13.75037163$ |
5.420905692 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}$ |
| 32.1-b2 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$3.65655$ |
$(2,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$13.56542070$ |
$27.50074327$ |
5.420905692 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \) |
${y}^2={x}^{3}-4{x}$ |
| 32.1-b3 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$3.65655$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$6.782710350$ |
$13.75037163$ |
5.420905692 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 124\) , \( 255\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+124{x}+255$ |
| 32.1-b4 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{74}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$3.65655$ |
$(2,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$6.782710350$ |
$55.00148654$ |
5.420905692 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 87\) , \( 240\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+87{x}+240$ |
*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.
