Properties

Label 25872.u
Number of curves $2$
Conductor $25872$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 25872.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25872.u1 25872i2 \([0, -1, 0, -21968, -1236192]\) \(4866277250/43659\) \(10519424391168\) \([2]\) \(73728\) \(1.3215\)  
25872.u2 25872i1 \([0, -1, 0, -408, -46080]\) \(-62500/7623\) \(-918362446848\) \([2]\) \(36864\) \(0.97495\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 25872.u have rank \(1\).

Complex multiplication

The elliptic curves in class 25872.u do not have complex multiplication.

Modular form 25872.2.a.u

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