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Properties

Label 139230ep
Number of curves $2$
Conductor $139230$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ep1")
 
E.isogeny_class()
 

Elliptic curves in class 139230ep

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139230.c2 139230ep1 \([1, -1, 0, -960, -10900]\) \(4973940243/154700\) \(3044960100\) \([2]\) \(116736\) \(0.59502\) \(\Gamma_0(N)\)-optimal
139230.c1 139230ep2 \([1, -1, 0, -2310, 27710]\) \(69274613043/23932090\) \(471055327470\) \([2]\) \(233472\) \(0.94160\)  

Rank

sage: E.rank()
 

The elliptic curves in class 139230ep have rank \(1\).

Complex multiplication

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

Modular form 139230.2.a.ep

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.