Properties

Label 16800.m
Number of curves $4$
Conductor $16800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 16800.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16800.m1 16800bj2 \([0, -1, 0, -1639408, -807355688]\) \(60910917333827912/3255076125\) \(26040609000000000\) \([2]\) \(221184\) \(2.2173\)  
16800.m2 16800bj3 \([0, -1, 0, -530033, 138659937]\) \(257307998572864/19456203375\) \(1245197016000000000\) \([4]\) \(221184\) \(2.2173\)  
16800.m3 16800bj1 \([0, -1, 0, -108158, -11105688]\) \(139927692143296/27348890625\) \(27348890625000000\) \([2, 2]\) \(110592\) \(1.8707\) \(\Gamma_0(N)\)-optimal
16800.m4 16800bj4 \([0, -1, 0, 222592, -66010188]\) \(152461584507448/322998046875\) \(-2583984375000000000\) \([2]\) \(221184\) \(2.2173\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16800.m have rank \(1\).

Complex multiplication

The elliptic curves in class 16800.m do not have complex multiplication.

Modular form 16800.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} - 4 q^{11} - 2 q^{13} + 2 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.