Properties

Label 180708.g
Number of curves $2$
Conductor $180708$
CM no
Rank $1$
Graph

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

Elliptic curves in class 180708.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
180708.g1 180708i2 \([0, -1, 0, -214697988, 1210920788808]\) \(1666315860501346000/40252707\) \(26439022946211625728\) \([2]\) \(15759360\) \(3.2468\)  
180708.g2 180708i1 \([0, -1, 0, -13434453, 18877123710]\) \(6532108386304000/31987847133\) \(1313153026499088566352\) \([2]\) \(7879680\) \(2.9002\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 180708.g have rank \(1\).

Complex multiplication

The elliptic curves in class 180708.g do not have complex multiplication.

Modular form 180708.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + q^{11} - 2 q^{13} + 4 q^{17} - 2 q^{19} + O(q^{20})\) 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.