Properties

Label 2880.z
Number of curves $4$
Conductor $2880$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.z1 2880q3 \([0, 0, 0, -5772, -168784]\) \(890277128/15\) \(358318080\) \([2]\) \(2048\) \(0.77168\)  
2880.z2 2880q4 \([0, 0, 0, -1452, 18704]\) \(14172488/1875\) \(44789760000\) \([4]\) \(2048\) \(0.77168\)  
2880.z3 2880q2 \([0, 0, 0, -372, -2464]\) \(1906624/225\) \(671846400\) \([2, 2]\) \(1024\) \(0.42511\)  
2880.z4 2880q1 \([0, 0, 0, 33, -196]\) \(85184/405\) \(-18895680\) \([2]\) \(512\) \(0.078535\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2880.z have rank \(1\).

Complex multiplication

The elliptic curves in class 2880.z do not have complex multiplication.

Modular form 2880.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{5} - 2 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.