Properties

Label 36300.ba
Number of curves $2$
Conductor $36300$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 36300.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36300.ba1 36300m2 \([0, -1, 0, -133355108, 592782218712]\) \(-2527934627152/9\) \(-933747285636000000\) \([]\) \(3592512\) \(3.0900\)  
36300.ba2 36300m1 \([0, -1, 0, -1586108, 875870712]\) \(-4253392/729\) \(-75633530136516000000\) \([]\) \(1197504\) \(2.5407\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 36300.ba have rank \(1\).

Complex multiplication

The elliptic curves in class 36300.ba do not have complex multiplication.

Modular form 36300.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{7} + q^{9} + 5 q^{13} - 3 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.