Properties

Label 35280.di
Number of curves $6$
Conductor $35280$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("di1")
 
E.isogeny_class()
 

Elliptic curves in class 35280.di

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35280.di1 35280cr6 \([0, 0, 0, -1411347, 645355186]\) \(1770025017602/75\) \(13173676185600\) \([2]\) \(393216\) \(2.0023\)  
35280.di2 35280cr4 \([0, 0, 0, -88347, 10050586]\) \(868327204/5625\) \(494012856960000\) \([2, 2]\) \(196608\) \(1.6557\)  
35280.di3 35280cr5 \([0, 0, 0, -35427, 21978754]\) \(-27995042/1171875\) \(-205838690400000000\) \([2]\) \(393216\) \(2.0023\)  
35280.di4 35280cr2 \([0, 0, 0, -8967, -62426]\) \(3631696/2025\) \(44461157126400\) \([2, 2]\) \(98304\) \(1.3091\)  
35280.di5 35280cr1 \([0, 0, 0, -6762, -213689]\) \(24918016/45\) \(61751607120\) \([2]\) \(49152\) \(0.96254\) \(\Gamma_0(N)\)-optimal
35280.di6 35280cr3 \([0, 0, 0, 35133, -494606]\) \(54607676/32805\) \(-2881082981790720\) \([2]\) \(196608\) \(1.6557\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35280.di have rank \(2\).

Complex multiplication

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

Modular form 35280.2.a.di

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4 q^{11} - 6 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.