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Properties

Label 8190h
Number of curves $2$
Conductor $8190$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 8190h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8190.c1 8190h1 \([1, -1, 0, -18495, -963495]\) \(959781554388721/19377540\) \(14126226660\) \([2]\) \(15360\) \(1.0679\) \(\Gamma_0(N)\)-optimal
8190.c2 8190h2 \([1, -1, 0, -17865, -1032669]\) \(-865005601073041/136840035150\) \(-99756385624350\) \([2]\) \(30720\) \(1.4145\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8190h have rank \(0\).

Complex multiplication

The elliptic curves in class 8190h do not have complex multiplication.

Modular form 8190.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} - 2 q^{11} - q^{13} + q^{14} + q^{16} + 4 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.