Properties

Label 277200.fq
Number of curves $4$
Conductor $277200$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("fq1")
 
E.isogeny_class()
 

Elliptic curves in class 277200.fq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277200.fq1 277200fq4 \([0, 0, 0, -7392675, -7736606750]\) \(957681397954009/31185\) \(1454967360000000\) \([2]\) \(4718592\) \(2.4108\)  
277200.fq2 277200fq3 \([0, 0, 0, -732675, 36333250]\) \(932288503609/527295615\) \(24601504213440000000\) \([2]\) \(4718592\) \(2.4108\)  
277200.fq3 277200fq2 \([0, 0, 0, -462675, -120536750]\) \(234770924809/1334025\) \(62240270400000000\) \([2, 2]\) \(2359296\) \(2.0642\)  
277200.fq4 277200fq1 \([0, 0, 0, -12675, -3986750]\) \(-4826809/144375\) \(-6735960000000000\) \([2]\) \(1179648\) \(1.7176\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 277200.fq have rank \(0\).

Complex multiplication

The elliptic curves in class 277200.fq do not have complex multiplication.

Modular form 277200.2.a.fq

sage: E.q_eigenform(10)
 
\(q - q^{7} + q^{11} + 2 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.