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Properties

Label 25230.k
Number of curves $2$
Conductor $25230$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 25230.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25230.k1 25230l1 \([1, 0, 1, -1480178, 679610756]\) \(602944222256641/13363200000\) \(7948743003187200000\) \([2]\) \(940800\) \(2.4143\) \(\Gamma_0(N)\)-optimal
25230.k2 25230l2 \([1, 0, 1, 134542, 2083771268]\) \(452807907839/3153750000000\) \(-1875924048603750000000\) \([2]\) \(1881600\) \(2.7609\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25230.k have rank \(1\).

Complex multiplication

The elliptic curves in class 25230.k do not have complex multiplication.

Modular form 25230.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 4 q^{7} - q^{8} + q^{9} - q^{10} + 4 q^{11} + q^{12} - 4 q^{13} + 4 q^{14} + q^{15} + q^{16} + 2 q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) 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 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.