Properties

Label 190575.eh
Number of curves $2$
Conductor $190575$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("eh1")
 
E.isogeny_class()
 

Elliptic curves in class 190575.eh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190575.eh1 190575dx2 \([1, -1, 0, -1815567, -899796034]\) \(24642171/1225\) \(32901659949301171875\) \([2]\) \(4866048\) \(2.5040\)  
190575.eh2 190575dx1 \([1, -1, 0, -318192, 51037091]\) \(132651/35\) \(940047427122890625\) \([2]\) \(2433024\) \(2.1574\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 190575.eh have rank \(1\).

Complex multiplication

The elliptic curves in class 190575.eh do not have complex multiplication.

Modular form 190575.2.a.eh

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{7} - 3 q^{8} + 4 q^{13} + q^{14} - q^{16} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.