Properties

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

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Show commands: SageMath
E = EllipticCurve("hf1")
 
E.isogeny_class()
 

Elliptic curves in class 227850hf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
227850.c1 227850hf1 \([1, 1, 0, -1822825, -1080402875]\) \(-14575072995625/2522463552\) \(-115923950948925000000\) \([]\) \(11197440\) \(2.5761\) \(\Gamma_0(N)\)-optimal
227850.c2 227850hf2 \([1, 1, 0, 12417800, 4635784000]\) \(4607967053654375/2868211089408\) \(-131813346272563200000000\) \([]\) \(33592320\) \(3.1254\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 227850.2.a.hf

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.