Properties

Label 30800ca
Number of curves 4
Conductor 30800
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("30800.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30800ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30800.u3 30800ca1 [0, 1, 0, -22408, -25132812] [2] 331776 \(\Gamma_0(N)\)-optimal
30800.u2 30800ca2 [0, 1, 0, -1430408, -653100812] [2] 663552  
30800.u4 30800ca3 [0, 1, 0, 201592, 676883188] [2] 995328  
30800.u1 30800ca4 [0, 1, 0, -10446408, 12623939188] [2] 1990656  

Rank

sage: E.rank()
 

The elliptic curves in class 30800ca have rank \(0\).

Modular form 30800.2.a.u

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{7} + q^{9} + q^{11} + 4q^{13} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.