Properties

Label 834g
Number of curves $2$
Conductor $834$
CM no
Rank $1$
Graph

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

Elliptic curves in class 834g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
834.g2 834g1 \([1, 0, 0, -70, 356]\) \(-37966934881/34587648\) \(-34587648\) \([5]\) \(400\) \(0.14336\) \(\Gamma_0(N)\)-optimal
834.g1 834g2 \([1, 0, 0, -1090, -40504]\) \(-143228059472161/622666136388\) \(-622666136388\) \([]\) \(2000\) \(0.94808\)  

Rank

sage: E.rank()
 

The elliptic curves in class 834g have rank \(1\).

Complex multiplication

The elliptic curves in class 834g do not have complex multiplication.

Modular form 834.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 4 q^{5} + q^{6} - 2 q^{7} + q^{8} + q^{9} - 4 q^{10} - 3 q^{11} + q^{12} - q^{13} - 2 q^{14} - 4 q^{15} + q^{16} - 7 q^{17} + q^{18} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.