Properties

Label 8820.h
Number of curves $4$
Conductor $8820$
CM no
Rank $1$
Graph

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

Elliptic curves in class 8820.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8820.h1 8820a4 \([0, 0, 0, -186543, 12428262]\) \(1210991472/588245\) \(348720711650922240\) \([2]\) \(82944\) \(2.0596\)  
8820.h2 8820a3 \([0, 0, 0, -153468, 23124717]\) \(10788913152/8575\) \(317712018632400\) \([2]\) \(41472\) \(1.7130\)  
8820.h3 8820a2 \([0, 0, 0, -98343, -11869858]\) \(129348709488/6125\) \(4980788064000\) \([2]\) \(27648\) \(1.5103\)  
8820.h4 8820a1 \([0, 0, 0, -6468, -164983]\) \(588791808/109375\) \(5558915250000\) \([2]\) \(13824\) \(1.1637\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8820.h have rank \(1\).

Complex multiplication

The elliptic curves in class 8820.h do not have complex multiplication.

Modular form 8820.2.a.h

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