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
225.1-c6 225.1-c $12$
$64$
\(\Q(\sqrt{3}, \sqrt{5})\) $4$
$[4, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{4} \cdot 5^{4} \)
$10.55146$
$(-2/7a^3+3/7a^2+19/7a-10/7), (4/7a^3-6/7a^2-24/7a+13/7)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $64$
\( 2^{2} \)
$1$
$6.492249124$
1.731266433
\( \frac{56667352321}{15} \)
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( 1\) , \( 0\) , \( -79\) , \( -322\bigr] \) ${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{10}{7}\right){x}{y}={x}^{3}+{x}^{2}-79{x}-322$
225.1-e7 225.1-e $12$
$64$
\(\Q(\sqrt{3}, \sqrt{5})\) $4$
$[4, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{4} \cdot 5^{4} \)
$10.55146$
$(-2/7a^3+3/7a^2+19/7a-10/7), (4/7a^3-6/7a^2-24/7a+13/7)$
$2$
$\Z/2\Z\oplus\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2^{2} \)
$0.780504772$
$985.1451572$
3.203793738
\( \frac{56667352321}{15} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
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Pari/GP
SageMath
Magma
Oscar
CSV
*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.
