Properties

Label 234416.g
Number of curves $2$
Conductor $234416$
CM no
Rank $0$
Graph

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

Elliptic curves in class 234416.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
234416.g1 234416g2 \([0, 1, 0, -141248, -20566988]\) \(-1552807715412625/7697866228\) \(-1544992543424512\) \([]\) \(1306368\) \(1.7623\)  
234416.g2 234416g1 \([0, 1, 0, 4352, -148044]\) \(45408227375/74381632\) \(-14928691068928\) \([]\) \(435456\) \(1.2130\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 234416.g have rank \(0\).

Complex multiplication

The elliptic curves in class 234416.g do not have complex multiplication.

Modular form 234416.2.a.g

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.