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Properties

Label 227430.eu
Number of curves $2$
Conductor $227430$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("eu1")
 
E.isogeny_class()
 

Elliptic curves in class 227430.eu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
227430.eu1 227430co1 \([1, -1, 1, -1849832, -965826389]\) \(551105805571803/1376829440\) \(1748902157771489280\) \([2]\) \(7338240\) \(2.3778\) \(\Gamma_0(N)\)-optimal
227430.eu2 227430co2 \([1, -1, 1, -1156712, -1698870101]\) \(-134745327251163/903920796800\) \(-1148195256471305481600\) \([2]\) \(14676480\) \(2.7244\)  

Rank

sage: E.rank()
 

The elliptic curves in class 227430.eu have rank \(0\).

Complex multiplication

The elliptic curves in class 227430.eu do not have complex multiplication.

Modular form 227430.2.a.eu

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} - 4 q^{11} - 6 q^{13} - q^{14} + q^{16} + 4 q^{17} + O(q^{20})\) 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.