Properties

Label 225400.cs
Number of curves $2$
Conductor $225400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 225400.cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
225400.cs1 225400bj2 \([0, -1, 0, -598208, -177871588]\) \(12576878500/1127\) \(2121446768000000\) \([2]\) \(2211840\) \(1.9809\)  
225400.cs2 225400bj1 \([0, -1, 0, -34708, -3186588]\) \(-9826000/3703\) \(-1742616988000000\) \([2]\) \(1105920\) \(1.6343\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 225400.cs have rank \(1\).

Complex multiplication

The elliptic curves in class 225400.cs do not have complex multiplication.

Modular form 225400.2.a.cs

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + q^{9} + 4q^{11} + 6q^{13} + O(q^{20})\)  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.