Properties

Label 80850.ci
Number of curves $4$
Conductor $80850$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ci1")
 
E.isogeny_class()
 

Elliptic curves in class 80850.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80850.ci1 80850by4 \([1, 0, 1, -60368026, 180528788948]\) \(13235378341603461121/9240\) \(16985574375000\) \([2]\) \(3538944\) \(2.7516\)  
80850.ci2 80850by2 \([1, 0, 1, -3773026, 2820488948]\) \(3231355012744321/85377600\) \(156946707225000000\) \([2, 2]\) \(1769472\) \(2.4051\)  
80850.ci3 80850by3 \([1, 0, 1, -3626026, 3050396948]\) \(-2868190647517441/527295615000\) \(-969309403267734375000\) \([2]\) \(3538944\) \(2.7516\)  
80850.ci4 80850by1 \([1, 0, 1, -245026, 40424948]\) \(885012508801/127733760\) \(234808580160000000\) \([2]\) \(884736\) \(2.0585\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 80850.ci have rank \(1\).

Complex multiplication

The elliptic curves in class 80850.ci do not have complex multiplication.

Modular form 80850.2.a.ci

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} - q^{11} + q^{12} + 2 q^{13} + q^{16} - 2 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.