↑

Properties

Label 333270.ca
Number of curves $2$
Conductor $333270$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 333270.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.ca1 333270ca2 \([1, -1, 0, -1374461124, 19613443359680]\) \(8099892914322789/12250000\) \(434288075985808805250000\) \([2]\) \(162791424\) \(3.8036\)  
333270.ca2 333270ca1 \([1, -1, 0, -86705844, 300462323408]\) \(2033419614309/76832000\) \(2723854812582992826528000\) \([2]\) \(81395712\) \(3.4571\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 333270.ca have rank \(0\).

Complex multiplication

The elliptic curves in class 333270.ca do not have complex multiplication.

Modular form 333270.2.a.ca

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} - 4 q^{11} - 2 q^{13} - q^{14} + q^{16} - 2 q^{17} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.