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Properties

Label 25410s
Number of curves $2$
Conductor $25410$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 25410s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25410.r1 25410s1 \([1, 1, 0, -595927, -177121259]\) \(9925899473771/12600000\) \(29710140906600000\) \([2]\) \(380160\) \(2.0691\) \(\Gamma_0(N)\)-optimal
25410.r2 25410s2 \([1, 1, 0, -436207, -274007411]\) \(-3892861862891/11484375000\) \(-27079555513828125000\) \([2]\) \(760320\) \(2.4157\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25410s have rank \(1\).

Complex multiplication

The elliptic curves in class 25410s do not have complex multiplication.

Modular form 25410.2.a.s

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