Properties

Label 270480ix
Number of curves $2$
Conductor $270480$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("ix1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 270480ix

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.ix1 270480ix1 \([0, 1, 0, -18440, 525300]\) \(1439069689/579600\) \(279303620198400\) \([2]\) \(884736\) \(1.4699\) \(\Gamma_0(N)\)-optimal
270480.ix2 270480ix2 \([0, 1, 0, 59960, 3880820]\) \(49471280711/41992020\) \(-20235547283374080\) \([2]\) \(1769472\) \(1.8165\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270480ix have rank \(0\).

Complex multiplication

The elliptic curves in class 270480ix do not have complex multiplication.

Modular form 270480.2.a.ix

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + 2q^{11} - 4q^{13} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.