Properties

Label 13860.g
Number of curves $2$
Conductor $13860$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13860.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.g1 13860b2 \([0, 0, 0, -8343, 210222]\) \(12745567728/3587045\) \(18074574524160\) \([2]\) \(32256\) \(1.2508\)  
13860.g2 13860b1 \([0, 0, 0, -7668, 258417]\) \(158328373248/21175\) \(6668600400\) \([2]\) \(16128\) \(0.90419\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 13860.g have rank \(1\).

Complex multiplication

The elliptic curves in class 13860.g do not have complex multiplication.

Modular form 13860.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} - q^{11} - 4q^{13} + 2q^{17} - 6q^{19} + O(q^{20})\)  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.