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Properties

Label 15925f
Number of curves $2$
Conductor $15925$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 15925f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15925.p1 15925f1 \([1, 0, 1, -1251, -3727]\) \(117649/65\) \(119487265625\) \([2]\) \(13824\) \(0.81606\) \(\Gamma_0(N)\)-optimal
15925.p2 15925f2 \([1, 0, 1, 4874, -28227]\) \(6967871/4225\) \(-7766672265625\) \([2]\) \(27648\) \(1.1626\)  

Rank

sage: E.rank()
 

The elliptic curves in class 15925f have rank \(0\).

Complex multiplication

The elliptic curves in class 15925f do not have complex multiplication.

Modular form 15925.2.a.f

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