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Properties

Label 25270y
Number of curves $2$
Conductor $25270$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 25270y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25270.x1 25270y1 \([1, 1, 1, -2540545, 1164459007]\) \(5619814620139/1433600000\) \(462605083535974400000\) \([2]\) \(1094400\) \(2.6748\) \(\Gamma_0(N)\)-optimal
25270.x2 25270y2 \([1, 1, 1, 6238975, 7454107135]\) \(83230218613781/122500000000\) \(-39529242977927500000000\) \([2]\) \(2188800\) \(3.0214\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25270y have rank \(0\).

Complex multiplication

The elliptic curves in class 25270y do not have complex multiplication.

Modular form 25270.2.a.y

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + q^{5} + 2 q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 4 q^{11} + 2 q^{12} + q^{14} + 2 q^{15} + q^{16} - 2 q^{17} + q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.