Properties

Label 2394.g
Number of curves $2$
Conductor $2394$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 2394.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2394.g1 2394o2 \([1, -1, 1, -5387, 153515]\) \(23711636464489/363888\) \(265274352\) \([2]\) \(4096\) \(0.75181\)  
2394.g2 2394o1 \([1, -1, 1, -347, 2315]\) \(6321363049/715008\) \(521240832\) \([2]\) \(2048\) \(0.40523\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2394.g have rank \(1\).

Complex multiplication

The elliptic curves in class 2394.g do not have complex multiplication.

Modular form 2394.2.a.g

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