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Properties

Label 86190.t
Number of curves $4$
Conductor $86190$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 86190.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86190.t1 86190r4 \([1, 1, 0, -1105432, -447803624]\) \(30949975477232209/478125000\) \(2307818053125000\) \([2]\) \(1769472\) \(2.0830\)  
86190.t2 86190r2 \([1, 1, 0, -71152, -6579776]\) \(8253429989329/936360000\) \(4519630875240000\) \([2, 2]\) \(884736\) \(1.7364\)  
86190.t3 86190r1 \([1, 1, 0, -17072, 742656]\) \(114013572049/15667200\) \(75622581964800\) \([2]\) \(442368\) \(1.3899\) \(\Gamma_0(N)\)-optimal
86190.t4 86190r3 \([1, 1, 0, 97848, -32909976]\) \(21464092074671/109596256200\) \(-529000195792465800\) \([2]\) \(1769472\) \(2.0830\)  

Rank

sage: E.rank()
 

The elliptic curves in class 86190.t have rank \(1\).

Complex multiplication

The elliptic curves in class 86190.t do not have complex multiplication.

Modular form 86190.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 4 q^{7} - q^{8} + q^{9} - q^{10} + 4 q^{11} - q^{12} - 4 q^{14} - q^{15} + q^{16} + q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.