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Properties

Label 139230el
Number of curves $2$
Conductor $139230$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("el1")
 
E.isogeny_class()
 

Elliptic curves in class 139230el

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139230.p2 139230el1 \([1, -1, 0, -36870, -2500300]\) \(281616734422323/24752000000\) \(487193616000000\) \([2]\) \(645120\) \(1.5587\) \(\Gamma_0(N)\)-optimal
139230.p1 139230el2 \([1, -1, 0, -576870, -168496300]\) \(1078615620856342323/9572836000\) \(188422130988000\) \([2]\) \(1290240\) \(1.9052\)  

Rank

sage: E.rank()
 

The elliptic curves in class 139230el have rank \(0\).

Complex multiplication

The elliptic curves in class 139230el do not have complex multiplication.

Modular form 139230.2.a.el

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} - 2 q^{11} + q^{13} - q^{14} + q^{16} + q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.