Properties

Label 277200et
Number of curves $4$
Conductor $277200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("et1")
 
E.isogeny_class()
 

Elliptic curves in class 277200et

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277200.et4 277200et1 \([0, 0, 0, -2320275, -450040750]\) \(29609739866953/15259926528\) \(711967132090368000000\) \([2]\) \(11796480\) \(2.6933\) \(\Gamma_0(N)\)-optimal
277200.et2 277200et2 \([0, 0, 0, -20752275, 36063751250]\) \(21184262604460873/216872764416\) \(10118415696592896000000\) \([2, 2]\) \(23592960\) \(3.0399\)  
277200.et1 277200et3 \([0, 0, 0, -331216275, 2320147399250]\) \(86129359107301290313/9166294368\) \(427662630033408000000\) \([2]\) \(47185920\) \(3.3865\)  
277200.et3 277200et4 \([0, 0, 0, -5200275, 88862791250]\) \(-333345918055753/72923718045024\) \(-3402328989108639744000000\) \([2]\) \(47185920\) \(3.3865\)  

Rank

sage: E.rank()
 

The elliptic curves in class 277200et have rank \(0\).

Complex multiplication

The elliptic curves in class 277200et do not have complex multiplication.

Modular form 277200.2.a.et

sage: E.q_eigenform(10)
 
\(q - q^{7} + q^{11} - 2 q^{13} + 6 q^{17} + 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.