Properties

Label 16245.c
Number of curves $8$
Conductor $16245$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 16245.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16245.c1 16245d7 \([1, -1, 1, -7017908, -7154068534]\) \(1114544804970241/405\) \(13890061135845\) \([2]\) \(221184\) \(2.3124\)  
16245.c2 16245d5 \([1, -1, 1, -438683, -111666094]\) \(272223782641/164025\) \(5625474760017225\) \([2, 2]\) \(110592\) \(1.9658\)  
16245.c3 16245d8 \([1, -1, 1, -357458, -154357954]\) \(-147281603041/215233605\) \(-7381747980094602645\) \([2]\) \(221184\) \(2.3124\)  
16245.c4 16245d4 \([1, -1, 1, -259988, 51089312]\) \(56667352321/15\) \(514446708735\) \([2]\) \(55296\) \(1.6192\)  
16245.c5 16245d3 \([1, -1, 1, -32558, -1037644]\) \(111284641/50625\) \(1736257641980625\) \([2, 2]\) \(55296\) \(1.6192\)  
16245.c6 16245d2 \([1, -1, 1, -16313, 794792]\) \(13997521/225\) \(7716700631025\) \([2, 2]\) \(27648\) \(1.2727\)  
16245.c7 16245d1 \([1, -1, 1, -68, 34526]\) \(-1/15\) \(-514446708735\) \([2]\) \(13824\) \(0.92610\) \(\Gamma_0(N)\)-optimal
16245.c8 16245d6 \([1, -1, 1, 113647, -7880038]\) \(4733169839/3515625\) \(-120573447359765625\) \([2]\) \(110592\) \(1.9658\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16245.c have rank \(1\).

Complex multiplication

The elliptic curves in class 16245.c do not have complex multiplication.

Modular form 16245.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} + 3 q^{8} + q^{10} + 4 q^{11} + 2 q^{13} - q^{16} - 2 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.