Properties

Label 180.a
Number of curves $4$
Conductor $180$
CM no
Rank $0$
Graph

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

Elliptic curves in class 180.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
180.a1 180a3 \([0, 0, 0, -372, 2761]\) \(488095744/125\) \(1458000\) \([6]\) \(36\) \(0.16866\)  
180.a2 180a4 \([0, 0, 0, -327, 3454]\) \(-20720464/15625\) \(-2916000000\) \([6]\) \(72\) \(0.51524\)  
180.a3 180a1 \([0, 0, 0, -12, -11]\) \(16384/5\) \(58320\) \([2]\) \(12\) \(-0.38064\) \(\Gamma_0(N)\)-optimal
180.a4 180a2 \([0, 0, 0, 33, -74]\) \(21296/25\) \(-4665600\) \([2]\) \(24\) \(-0.034070\)  

Rank

sage: E.rank()
 

The elliptic curves in class 180.a have rank \(0\).

Complex multiplication

The elliptic curves in class 180.a do not have complex multiplication.

Modular form 180.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2q^{7} + 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.