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Properties

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

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 227850.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
227850.r1 227850hi2 \([1, 1, 0, -8824925, 10019929725]\) \(430523082386425/3294646272\) \(581660016281326080000\) \([]\) \(14370048\) \(2.8137\)  
227850.r2 227850hi1 \([1, 1, 0, -721550, -227598300]\) \(235322540425/9762768\) \(1723587701080770000\) \([]\) \(4790016\) \(2.2644\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 227850.2.a.r

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.