Properties

Label 111090.bc
Number of curves $4$
Conductor $111090$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 111090.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111090.bc1 111090bd4 \([1, 0, 1, -1594754358, -67378296632]\) \(3029968325354577848895529/1753440696000000000000\) \(259572152241138744000000000000\) \([2]\) \(145981440\) \(4.3335\)  
111090.bc2 111090bd2 \([1, 0, 1, -1097063223, -13986080583494]\) \(986396822567235411402169/6336721794060000\) \(938062244129347019340000\) \([2]\) \(48660480\) \(3.7842\)  
111090.bc3 111090bd1 \([1, 0, 1, -67248343, -227341860742]\) \(-227196402372228188089/19338934824115200\) \(-2862856409000952270412800\) \([2]\) \(24330240\) \(3.4377\) \(\Gamma_0(N)\)-optimal
111090.bc4 111090bd3 \([1, 0, 1, 398686922, -8372434744]\) \(47342661265381757089751/27397579603968000000\) \(-4055825053121670807552000000\) \([2]\) \(72990720\) \(3.9870\)  

Rank

sage: E.rank()
 

The elliptic curves in class 111090.bc have rank \(0\).

Complex multiplication

The elliptic curves in class 111090.bc do not have complex multiplication.

Modular form 111090.2.a.bc

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + q^{12} - 4q^{13} + q^{14} + q^{15} + q^{16} - q^{18} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.