Properties

Label 15680.cm
Number of curves $3$
Conductor $15680$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680.cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.cm1 15680j3 \([0, 1, 0, -25741, 1654309]\) \(-250523582464/13671875\) \(-102942875000000\) \([]\) \(41472\) \(1.4470\)  
15680.cm2 15680j1 \([0, 1, 0, -261, -1891]\) \(-262144/35\) \(-263533760\) \([]\) \(4608\) \(0.34838\) \(\Gamma_0(N)\)-optimal
15680.cm3 15680j2 \([0, 1, 0, 1699, 5165]\) \(71991296/42875\) \(-322828856000\) \([]\) \(13824\) \(0.89769\)  

Rank

sage: E.rank()
 

The elliptic curves in class 15680.cm have rank \(0\).

Complex multiplication

The elliptic curves in class 15680.cm do not have complex multiplication.

Modular form 15680.2.a.cm

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 2q^{9} + 3q^{11} + 5q^{13} - q^{15} - 3q^{17} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.