Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("lk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 277200.lk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277200.lk1 277200lk4 \([0, 0, 0, -23957200875, 1427216919156250]\) \(260744057755293612689909/8504954620259328\) \(49600895345352400896000000000\) \([2]\) \(368640000\) \(4.6002\)  
277200.lk2 277200lk3 \([0, 0, 0, -1562320875, 20258583156250]\) \(72313087342699809269/11447096545640448\) \(66759467054175092736000000000\) \([2]\) \(184320000\) \(4.2536\)  
277200.lk3 277200lk2 \([0, 0, 0, -423910875, -3328601093750]\) \(1444540994277943589/15251205665388\) \(88945031440542816000000000\) \([2]\) \(73728000\) \(3.7955\)  
277200.lk4 277200lk1 \([0, 0, 0, -422830875, -3346556093750]\) \(1433528304665250149/162339408\) \(946763427456000000000\) \([2]\) \(36864000\) \(3.4489\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 277200.2.a.lk

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

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.