Properties

Label 8280.g
Number of curves $6$
Conductor $8280$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8280.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.g1 8280i5 \([0, 0, 0, -7837923, 8148740222]\) \(35667215800077781442/1427217706746225\) \(2130824618430459955200\) \([2]\) \(344064\) \(2.8590\)  
8280.g2 8280i3 \([0, 0, 0, -1276923, -384496378]\) \(308453964046598884/92949363050625\) \(69386327719839360000\) \([2, 2]\) \(172032\) \(2.5124\)  
8280.g3 8280i2 \([0, 0, 0, -1164423, -483563878]\) \(935596404100595536/150641015625\) \(28113228900000000\) \([2, 2]\) \(86016\) \(2.1658\)  
8280.g4 8280i1 \([0, 0, 0, -1164378, -483603127]\) \(14967807005098080256/388125\) \(4527090000\) \([2]\) \(43008\) \(1.8192\) \(\Gamma_0(N)\)-optimal
8280.g5 8280i4 \([0, 0, 0, -1052643, -580119442]\) \(-172798332611391364/94757080078125\) \(-70735781250000000000\) \([2]\) \(172032\) \(2.5124\)  
8280.g6 8280i6 \([0, 0, 0, 3484077, -2577412978]\) \(3132776881711582558/3735130619961225\) \(-5576520134557149235200\) \([2]\) \(344064\) \(2.8590\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8280.g have rank \(1\).

Complex multiplication

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

Modular form 8280.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{11} - 2 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.