Properties

Label 36400.co
Number of curves $2$
Conductor $36400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("co1")
 
E.isogeny_class()
 

Elliptic curves in class 36400.co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36400.co1 36400q1 \([0, -1, 0, -11908, -458688]\) \(46689225424/3901625\) \(15606500000000\) \([2]\) \(110592\) \(1.2735\) \(\Gamma_0(N)\)-optimal
36400.co2 36400q2 \([0, -1, 0, 12592, -2124688]\) \(13799183324/129390625\) \(-2070250000000000\) \([2]\) \(221184\) \(1.6201\)  

Rank

sage: E.rank()
 

The elliptic curves in class 36400.co have rank \(1\).

Complex multiplication

The elliptic curves in class 36400.co do not have complex multiplication.

Modular form 36400.2.a.co

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{7} + q^{9} - 6 q^{11} + q^{13} + 2 q^{17} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.