Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.i1 2880z3 \([0, 0, 0, -2028, -34832]\) \(38614472/405\) \(9674588160\) \([2]\) \(2048\) \(0.73261\)  
2880.i2 2880z2 \([0, 0, 0, -228, 448]\) \(438976/225\) \(671846400\) \([2, 2]\) \(1024\) \(0.38604\)  
2880.i3 2880z1 \([0, 0, 0, -183, 952]\) \(14526784/15\) \(699840\) \([2]\) \(512\) \(0.039465\) \(\Gamma_0(N)\)-optimal
2880.i4 2880z4 \([0, 0, 0, 852, 3472]\) \(2863288/1875\) \(-44789760000\) \([2]\) \(2048\) \(0.73261\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2880.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4q^{11} - 2q^{13} + 2q^{17} + 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.