Properties

Label 33600.eo
Number of curves $8$
Conductor $33600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("eo1")
 
E.isogeny_class()
 

Elliptic curves in class 33600.eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.eo1 33600cc8 \([0, 1, 0, -10321633, 8026548863]\) \(29689921233686449/10380965400750\) \(42520434281472000000000\) \([2]\) \(2654208\) \(3.0435\)  
33600.eo2 33600cc5 \([0, 1, 0, -9217633, 10768452863]\) \(21145699168383889/2593080\) \(10621255680000000\) \([2]\) \(884736\) \(2.4942\)  
33600.eo3 33600cc6 \([0, 1, 0, -4321633, -3367451137]\) \(2179252305146449/66177562500\) \(271063296000000000000\) \([2, 2]\) \(1327104\) \(2.6969\)  
33600.eo4 33600cc3 \([0, 1, 0, -4289633, -3421051137]\) \(2131200347946769/2058000\) \(8429568000000000\) \([2]\) \(663552\) \(2.3503\)  
33600.eo5 33600cc2 \([0, 1, 0, -577633, 167172863]\) \(5203798902289/57153600\) \(234101145600000000\) \([2, 2]\) \(442368\) \(2.1476\)  
33600.eo6 33600cc4 \([0, 1, 0, -129633, 420292863]\) \(-58818484369/18600435000\) \(-76187381760000000000\) \([2]\) \(884736\) \(2.4942\)  
33600.eo7 33600cc1 \([0, 1, 0, -65633, -2299137]\) \(7633736209/3870720\) \(15854469120000000\) \([2]\) \(221184\) \(1.8010\) \(\Gamma_0(N)\)-optimal
33600.eo8 33600cc7 \([0, 1, 0, 1166367, -11330539137]\) \(42841933504271/13565917968750\) \(-55566000000000000000000\) \([2]\) \(2654208\) \(3.0435\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 33600.2.a.eo

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} + 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.