Properties

Label 8280.r
Number of curves $4$
Conductor $8280$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8280.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.r1 8280k4 \([0, 0, 0, -19441587, 32994813166]\) \(544328872410114151778/14166950625\) \(21151143947520000\) \([2]\) \(196608\) \(2.6479\)  
8280.r2 8280k3 \([0, 0, 0, -1887267, -115818626]\) \(497927680189263938/284271240234375\) \(424414687500000000000\) \([2]\) \(196608\) \(2.6479\)  
8280.r3 8280k2 \([0, 0, 0, -1216587, 514218166]\) \(266763091319403556/1355769140625\) \(1012076240400000000\) \([2, 2]\) \(98304\) \(2.3013\)  
8280.r4 8280k1 \([0, 0, 0, -35607, 16553194]\) \(-26752376766544/618796614375\) \(-115482299361120000\) \([2]\) \(49152\) \(1.9547\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8280.r have rank \(0\).

Complex multiplication

The elliptic curves in class 8280.r do not have complex multiplication.

Modular form 8280.2.a.r

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