Properties

Label 33600eq
Number of curves 8
Conductor 33600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33600.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600eq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.i7 33600eq1 [0, -1, 0, 335967, -56592063] [2] 589824 \(\Gamma_0(N)\)-optimal
33600.i6 33600eq2 [0, -1, 0, -1712033, -505104063] [2, 2] 1179648  
33600.i5 33600eq3 [0, -1, 0, -12080033, 15803759937] [2, 2] 2359296  
33600.i4 33600eq4 [0, -1, 0, -24112033, -45551504063] [2] 2359296  
33600.i8 33600eq5 [0, -1, 0, 2031967, 50505167937] [2] 4718592  
33600.i2 33600eq6 [0, -1, 0, -192080033, 1024703759937] [2, 2] 4718592  
33600.i3 33600eq7 [0, -1, 0, -190880033, 1038137759937] [2] 9437184  
33600.i1 33600eq8 [0, -1, 0, -3073280033, 65577989759937] [2] 9437184  

Rank

sage: E.rank()
 

The elliptic curves in class 33600eq have rank \(0\).

Modular form 33600.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{7} + q^{9} - 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.