Properties

Label 296208.eg
Number of curves $2$
Conductor $296208$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("eg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 296208.eg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
296208.eg1 296208eg1 [0, 0, 0, -15751659, -23872137190] [2] 25804800 \(\Gamma_0(N)\)-optimal
296208.eg2 296208eg2 [0, 0, 0, -4600299, -57016209382] [2] 51609600  

Rank

sage: E.rank()
 

The elliptic curves in class 296208.eg have rank \(0\).

Complex multiplication

The elliptic curves in class 296208.eg do not have complex multiplication.

Modular form 296208.2.a.eg

sage: E.q_eigenform(10)
 
\( q + 2q^{5} - 4q^{7} + 4q^{13} - q^{17} - 8q^{19} + O(q^{20}) \)

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.