Properties

Label 334620.ch
Number of curves $4$
Conductor $334620$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ch1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 334620.ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
334620.ch1 334620ch4 \([0, 0, 0, -10799607, 13660291294]\) \(154639330142416/33275\) \(29974066853702400\) \([2]\) \(11197440\) \(2.5462\)  
334620.ch2 334620ch3 \([0, 0, 0, -677352, 211863301]\) \(610462990336/8857805\) \(498693537278473680\) \([2]\) \(5598720\) \(2.1997\)  
334620.ch3 334620ch2 \([0, 0, 0, -152607, 12966694]\) \(436334416/171875\) \(154824725484000000\) \([2]\) \(3732480\) \(1.9969\)  
334620.ch4 334620ch1 \([0, 0, 0, -68952, -6826079]\) \(643956736/15125\) \(851535990162000\) \([2]\) \(1866240\) \(1.6504\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 334620.ch have rank \(0\).

Complex multiplication

The elliptic curves in class 334620.ch do not have complex multiplication.

Modular form 334620.2.a.ch

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4q^{7} - q^{11} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.