Properties

Label 303600z
Number of curves 2
Conductor 303600
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("303600.z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 303600z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
303600.z2 303600z1 [0, -1, 0, -9208, 4948912] [2] 1474560 \(\Gamma_0(N)\)-optimal
303600.z1 303600z2 [0, -1, 0, -495208, 133252912] [2] 2949120  

Rank

sage: E.rank()
 

The elliptic curves in class 303600z have rank \(1\).

Modular form 303600.2.a.z

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.