Properties

Label 333795.bc
Number of curves $4$
Conductor $333795$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 333795.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333795.bc1 333795bc3 \([1, 0, 0, -254615, 49429452]\) \(75627935783569/396165\) \(9562460022885\) \([2]\) \(1769472\) \(1.6868\)  
333795.bc2 333795bc2 \([1, 0, 0, -16190, 743067]\) \(19443408769/1334025\) \(32200120485225\) \([2, 2]\) \(884736\) \(1.3402\)  
333795.bc3 333795bc1 \([1, 0, 0, -3185, -55440]\) \(148035889/31185\) \(752730089265\) \([2]\) \(442368\) \(0.99360\) \(\Gamma_0(N)\)-optimal
333795.bc4 333795bc4 \([1, 0, 0, 14155, 3213150]\) \(12994449551/192163125\) \(-4638350688943125\) \([2]\) \(1769472\) \(1.6868\)  

Rank

sage: E.rank()
 

The elliptic curves in class 333795.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 333795.bc do not have complex multiplication.

Modular form 333795.2.a.bc

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} + q^{5} - q^{6} + q^{7} + 3 q^{8} + q^{9} - q^{10} + q^{11} - q^{12} - 2 q^{13} - q^{14} + q^{15} - q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.