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 |
275.1-a1 |
275.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$3.19313$ |
$(a-6), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.540805159$ |
$16.93058676$ |
2.972859409 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+{x}$ |
275.1-a2 |
275.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$3.19313$ |
$(a-6), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.081610318$ |
$16.93058676$ |
2.972859409 |
\( \frac{8120601}{3025} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -4\) , \( 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-4{x}+3$ |
275.1-a3 |
275.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{2} \cdot 11^{8} \) |
$3.19313$ |
$(a-6), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$6.163220637$ |
$4.232646692$ |
2.972859409 |
\( \frac{2749884201}{73205} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -29\) , \( -52\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-29{x}-52$ |
275.1-a4 |
275.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$3.19313$ |
$(a-6), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.540805159$ |
$16.93058676$ |
2.972859409 |
\( \frac{22930509321}{6875} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -59\) , \( 190\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-59{x}+190$ |
275.1-b1 |
275.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$3.19313$ |
$(a-6), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$5.638786672$ |
$11.85112914$ |
1.903882058 |
\( \frac{59319}{55} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -9 a + 44\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a+44\right){x}$ |
275.1-b2 |
275.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$3.19313$ |
$(a-6), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.819393336$ |
$11.85112914$ |
1.903882058 |
\( \frac{8120601}{3025} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -36 a - 141\) , \( -276 a - 1074\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-36a-141\right){x}-276a-1074$ |
275.1-b3 |
275.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{2} \cdot 11^{8} \) |
$3.19313$ |
$(a-6), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.409696668$ |
$11.85112914$ |
1.903882058 |
\( \frac{2749884201}{73205} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 261 a - 1276\) , \( -4160 a + 20332\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(261a-1276\right){x}-4160a+20332$ |
275.1-b4 |
275.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$3.19313$ |
$(a-6), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.409696668$ |
$2.962782285$ |
1.903882058 |
\( \frac{22930509321}{6875} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -531 a - 2066\) , \( -15731 a - 61156\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-531a-2066\right){x}-15731a-61156$ |
*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.