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Properties

Label 238206i
Number of curves $2$
Conductor $238206$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 238206i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
238206.i2 238206i1 \([1, 0, 1, -1398, 6943624]\) \(-117649/8118144\) \(-20828936452864896\) \([]\) \(1446480\) \(1.8102\) \(\Gamma_0(N)\)-optimal
238206.i1 238206i2 \([1, 0, 1, -8913588, -10273698776]\) \(-30526075007211889/103499257854\) \(-265550779187908466286\) \([]\) \(10125360\) \(2.7831\)  

Rank

sage: E.rank()
 

The elliptic curves in class 238206i have rank \(0\).

Complex multiplication

The elliptic curves in class 238206i do not have complex multiplication.

Modular form 238206.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - q^{10} - 2 q^{11} + q^{12} - q^{14} + q^{15} + q^{16} + 3 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.