Properties

Label 720.h
Number of curves $4$
Conductor $720$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 720.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
720.h1 720i3 \([0, 0, 0, -372, -2761]\) \(488095744/125\) \(1458000\) \([2]\) \(144\) \(0.16866\)  
720.h2 720i4 \([0, 0, 0, -327, -3454]\) \(-20720464/15625\) \(-2916000000\) \([2]\) \(288\) \(0.51524\)  
720.h3 720i1 \([0, 0, 0, -12, 11]\) \(16384/5\) \(58320\) \([2]\) \(48\) \(-0.38064\) \(\Gamma_0(N)\)-optimal
720.h4 720i2 \([0, 0, 0, 33, 74]\) \(21296/25\) \(-4665600\) \([2]\) \(96\) \(-0.034070\)  

Rank

sage: E.rank()
 

The elliptic curves in class 720.h have rank \(0\).

Complex multiplication

The elliptic curves in class 720.h do not have complex multiplication.

Modular form 720.2.a.h

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.