Properties

Label 227850.hh
Number of curves $2$
Conductor $227850$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("hh1")
 
E.isogeny_class()
 

Elliptic curves in class 227850.hh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
227850.hh1 227850y2 \([1, 0, 0, -2465338, 521842292]\) \(901456690969801/457629750000\) \(841245038402343750000\) \([2]\) \(16588800\) \(2.7076\)  
227850.hh2 227850y1 \([1, 0, 0, 572662, 63104292]\) \(11298232190519/7472736000\) \(-13736873713500000000\) \([2]\) \(8294400\) \(2.3610\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 227850.hh have rank \(1\).

Complex multiplication

The elliptic curves in class 227850.hh do not have complex multiplication.

Modular form 227850.2.a.hh

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} - 4 q^{11} + q^{12} - 4 q^{13} + q^{16} + 2 q^{17} + q^{18} + 8 q^{19} + O(q^{20})\) 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.