Properties

Label 35280.cv
Number of curves $4$
Conductor $35280$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cv1")
 
E.isogeny_class()
 

Elliptic curves in class 35280.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35280.cv1 35280el4 \([0, 0, 0, -1888803, 999095202]\) \(2121328796049/120050\) \(42173328695500800\) \([2]\) \(589824\) \(2.2544\)  
35280.cv2 35280el3 \([0, 0, 0, -618723, -175051422]\) \(74565301329/5468750\) \(1921161110400000000\) \([2]\) \(589824\) \(2.2544\)  
35280.cv3 35280el2 \([0, 0, 0, -124803, 13724802]\) \(611960049/122500\) \(43034008872960000\) \([2, 2]\) \(294912\) \(1.9078\)  
35280.cv4 35280el1 \([0, 0, 0, 16317, 1278018]\) \(1367631/2800\) \(-983634488524800\) \([2]\) \(147456\) \(1.5612\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35280.cv have rank \(0\).

Complex multiplication

The elliptic curves in class 35280.cv do not have complex multiplication.

Modular form 35280.2.a.cv

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{11} + 6 q^{13} + 2 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.