Properties

Label 15680.n
Number of curves $4$
Conductor $15680$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.n1 15680s3 \([0, 1, 0, -8101, 277899]\) \(488095744/125\) \(15059072000\) \([2]\) \(17280\) \(0.93888\)  
15680.n2 15680s4 \([0, 1, 0, -7121, 348655]\) \(-20720464/15625\) \(-30118144000000\) \([2]\) \(34560\) \(1.2855\)  
15680.n3 15680s1 \([0, 1, 0, -261, -1205]\) \(16384/5\) \(602362880\) \([2]\) \(5760\) \(0.38958\) \(\Gamma_0(N)\)-optimal
15680.n4 15680s2 \([0, 1, 0, 719, -7281]\) \(21296/25\) \(-48189030400\) \([2]\) \(11520\) \(0.73615\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 15680.2.a.n

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.