Properties

Label 200277h
Number of curves $2$
Conductor $200277$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 200277h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
200277.i2 200277h1 \([1, -1, 1, 9049, -1259530]\) \(4657463/41503\) \(-730298732604903\) \([2]\) \(709632\) \(1.5333\) \(\Gamma_0(N)\)-optimal
200277.i1 200277h2 \([1, -1, 1, -134006, -17396134]\) \(15124197817/1294139\) \(22772042298498339\) \([2]\) \(1419264\) \(1.8799\)  

Rank

sage: E.rank()
 

The elliptic curves in class 200277h have rank \(0\).

Complex multiplication

The elliptic curves in class 200277h do not have complex multiplication.

Modular form 200277.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - 2 q^{5} + q^{7} + 3 q^{8} + 2 q^{10} + q^{11} + 4 q^{13} - q^{14} - q^{16} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.