Properties

Label 39600ed
Number of curves 4
Conductor 39600
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("39600.fb1")
sage: E.isogeny_class()

Elliptic curves in class 39600ed

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
39600.fb3 39600ed1 [0, 0, 0, -23475, -1372750] 2 98304 \(\Gamma_0(N)\)-optimal
39600.fb2 39600ed2 [0, 0, 0, -41475, 1021250] 4 196608  
39600.fb4 39600ed3 [0, 0, 0, 156525, 7951250] 2 393216  
39600.fb1 39600ed4 [0, 0, 0, -527475, 147307250] 2 393216  

Rank

sage: E.rank()

The elliptic curves in class 39600ed have rank \(0\).

Modular form 39600.2.a.fb

sage: E.q_eigenform(10)
\( q + 4q^{7} + q^{11} + 2q^{13} - 2q^{17} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.