Properties

Label 209300.i
Number of curves $2$
Conductor $209300$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 209300.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
209300.i1 209300h2 \([0, 0, 0, -8375, 24750]\) \(16241202000/9332687\) \(37330748000000\) \([2]\) \(414720\) \(1.2939\)  
209300.i2 209300h1 \([0, 0, 0, -5500, -156375]\) \(73598976000/336973\) \(84243250000\) \([2]\) \(207360\) \(0.94729\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 209300.i have rank \(1\).

Complex multiplication

The elliptic curves in class 209300.i do not have complex multiplication.

Modular form 209300.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{7} - 3q^{9} + q^{13} - 6q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.