Properties

Label 33600.co
Number of curves $4$
Conductor $33600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("co1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600.co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.co1 33600fd4 \([0, -1, 0, -2229633, -792748863]\) \(2394165105226952/854262178245\) \(437382235261440000000\) \([2]\) \(1474560\) \(2.6615\)  
33600.co2 33600fd2 \([0, -1, 0, -1984633, -1075233863]\) \(13507798771700416/3544416225\) \(226842638400000000\) \([2, 2]\) \(737280\) \(2.3150\)  
33600.co3 33600fd1 \([0, -1, 0, -1984508, -1075376238]\) \(864335783029582144/59535\) \(59535000000\) \([2]\) \(368640\) \(1.9684\) \(\Gamma_0(N)\)-optimal
33600.co4 33600fd3 \([0, -1, 0, -1741633, -1348608863]\) \(-1141100604753992/875529151875\) \(-448270925760000000000\) \([2]\) \(1474560\) \(2.6615\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33600.co have rank \(1\).

Complex multiplication

The elliptic curves in class 33600.co do not have complex multiplication.

Modular form 33600.2.a.co

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} - 4q^{11} - 6q^{13} - 6q^{17} + O(q^{20})\)  Toggle raw display

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.