Properties

Label 121275.bt
Number of curves $6$
Conductor $121275$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bt1")
 
E.isogeny_class()
 

Elliptic curves in class 121275.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121275.bt1 121275en6 \([1, -1, 1, -33617430230, -2372429651687728]\) \(3135316978843283198764801/571725\) \(766166180136328125\) \([2]\) \(70778880\) \(4.2261\)  
121275.bt2 121275en4 \([1, -1, 1, -2101089605, -37068811375228]\) \(765458482133960722801/326869475625\) \(438036359338442197265625\) \([2, 2]\) \(35389440\) \(3.8795\)  
121275.bt3 121275en5 \([1, -1, 1, -2090670980, -37454633896228]\) \(-754127868744065783521/15825714261328125\) \(-21207970691382712335205078125\) \([2]\) \(70778880\) \(4.2261\)  
121275.bt4 121275en3 \([1, -1, 1, -280531355, 953779972772]\) \(1821931919215868881/761147600816295\) \(1020010581726094620963984375\) \([2]\) \(35389440\) \(3.8795\)  
121275.bt5 121275en2 \([1, -1, 1, -131969480, -573138978478]\) \(189674274234120481/3859869269025\) \(5172593980802807844140625\) \([2, 2]\) \(17694720\) \(3.5330\)  
121275.bt6 121275en1 \([1, -1, 1, 385645, -26777022478]\) \(4733169839/231139696095\) \(-309749299112296835859375\) \([2]\) \(8847360\) \(3.1864\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 121275.bt have rank \(0\).

Complex multiplication

The elliptic curves in class 121275.bt do not have complex multiplication.

Modular form 121275.2.a.bt

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 3 q^{8} + q^{11} - 2 q^{13} - q^{16} - 2 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.