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Properties

Label 79350.dg
Number of curves $2$
Conductor $79350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dg1")
 
E.isogeny_class()
 

Elliptic curves in class 79350.dg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79350.dg1 79350dh2 \([1, 0, 0, -416863, -103547533]\) \(3463512697/3174\) \(7341654870093750\) \([2]\) \(1081344\) \(1.9679\)  
79350.dg2 79350dh1 \([1, 0, 0, -20113, -2376283]\) \(-389017/828\) \(-1915214313937500\) \([2]\) \(540672\) \(1.6213\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 79350.dg have rank \(0\).

Complex multiplication

The elliptic curves in class 79350.dg do not have complex multiplication.

Modular form 79350.2.a.dg

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