Properties

Label 360.a
Number of curves $4$
Conductor $360$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 360.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
360.a1 360e3 \([0, 0, 0, -963, 11502]\) \(132304644/5\) \(3732480\) \([2]\) \(128\) \(0.34709\)  
360.a2 360e2 \([0, 0, 0, -63, 162]\) \(148176/25\) \(4665600\) \([2, 2]\) \(64\) \(0.00051877\)  
360.a3 360e1 \([0, 0, 0, -18, -27]\) \(55296/5\) \(58320\) \([2]\) \(32\) \(-0.34606\) \(\Gamma_0(N)\)-optimal
360.a4 360e4 \([0, 0, 0, 117, 918]\) \(237276/625\) \(-466560000\) \([2]\) \(128\) \(0.34709\)  

Rank

sage: E.rank()
 

The elliptic curves in class 360.a have rank \(1\).

Complex multiplication

The elliptic curves in class 360.a do not have complex multiplication.

Modular form 360.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.